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1. <?xml version='1.0' encoding='UTF-8'?><?xml-stylesheet href="http://www.blogger.com/styles/atom.css" type="text/css"?><feed xmlns='http://www.w3.org/2005/Atom' xmlns:openSearch='http://a9.com/-/spec/opensearchrss/1.0/' xmlns:blogger='http://schemas.google.com/blogger/2008' xmlns:georss='http://www.georss.org/georss' xmlns:gd="http://schemas.google.com/g/2005" xmlns:thr='http://purl.org/syndication/thread/1.0'><id>tag:blogger.com,1999:blog-6749100220509682424</id><updated>2023-11-15T07:16:09.894-08:00</updated><category term="matematica"/><category term="geometria"/><category term="esempi svolti"/><category term="esercizi di matematica svolti"/><category term="esercizzi di matematica con soluzione"/><category term="algebra"/><category term="medie"/><category term="geometria analitica"/><category term="matematica III"/><category term="Geometria del piano"/><category term="Geometria dello spazio"/><category term="esercizi sistema lineare"/><category term="esercizi sistemi lineari omogenei"/><category term="esercizio diagonalizazione"/><category term="esercizi determinante"/><category term="media I"/><category term="Calcolo combinatorio"/><category term="Sottospazio"/><category term="matrici"/><category term="tavola dei NUMERI PRIMI da 2 a 5000"/><category term="Anelli"/><category term="Aritmetica"/><category term="Autospazio"/><category term="Autovettore Autovalore"/><category term="Base Ortonormale"/><category term="Calcolo dell&#39;Inversa di una Matrice"/><category term="Campi"/><category term="Caratterizzazione Diagonalizzazione"/><category term="Classe 1"/><category term="Definizione Omomorfismo"/><category term="Diagonalizzazione"/><category term="Diagonalizzazione Endomorfismi"/><category term="Diagonalizzazione Ortogonale"/><category term="Disuguaglianza Cauchy Schwarz"/><category term="EQUAZIONI E DISEQUAZIONI"/><category term="FORMULARIO: tavola degli integrali indefiniti"/><category term="FORMULARIO: tavola dei NUMERI PRIMI da 2 a 5000"/><category term="Geometria Solida. Parti della sfera e della superficie sferica"/><category term="Geometria Solida. Poliedri"/><category term="Geometria Solida. Poliedri regolari"/><category term="Geometria Solida. Poliedri. Piramide e tronco di piramide"/><category term="Geometria Solida. Poliedri. Prisma"/><category term="Geometria Solida. Solidi di rotazione. 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Cambiamento di riferimento. Traslazione"/><category term="giochi logici"/><category term="i numeri"/><category term="iperbole"/><category term="la retta"/><category term="matematica IV"/><category term="matrici determinante"/><category term="matrici esercizzi"/><category term="parabola"/><category term="parallelpipedo"/><category term="principali criteri di divisibilità dei numeri interi"/><category term="proporzioni e proprietà"/><category term="punti di accumulazione"/><category term="rotazione"/><category term="rototraslazione e coordinate polari"/><category term="sfera"/><category term="spazi vettoriali GeneralitaSottospazi"/><category term="spazio euclideo - Angolo"/><category term="tronco di cono"/><title type='text'>solo matematica</title><subtitle type='html'></subtitle><link rel='http://schemas.google.com/g/2005#feed' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/posts/default'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default?redirect=false'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/'/><link rel='hub' href='http://pubsubhubbub.appspot.com/'/><link rel='next' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default?start-index=26&amp;max-results=25&amp;redirect=false'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><generator version='7.00' uri='http://www.blogger.com'>Blogger</generator><openSearch:totalResults>155</openSearch:totalResults><openSearch:startIndex>1</openSearch:startIndex><openSearch:itemsPerPage>25</openSearch:itemsPerPage><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-6566471091033386027</id><published>2016-03-13T16:46:00.000-07:00</published><updated>2016-03-13T16:47:45.471-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="geometria analitica"/><category scheme="http://www.blogger.com/atom/ns#" term="geometria analitica. Cambiamento di riferimento. Traslazione"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><category scheme="http://www.blogger.com/atom/ns#" term="rotazione"/><category scheme="http://www.blogger.com/atom/ns#" term="rototraslazione e coordinate polari"/><title type='text'>geometria analitica. Cambiamento di riferimento. Traslazione, rotazione, rototraslazione e coordinate polari</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
2. <table align="center" border="0" cellpadding="5" cellspacing="1" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
3. <tr><td align="left" class="dividisotto" colspan="2" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" valign="top"><b><span style="color: #0b5394;">Formule per la traslazione degli assi</span></b><br />
4. <span style="color: #0b5394;">Le coordinate del generico punto P sono:<br /><img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image238.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="50" /> nel sistema di assi cartesiani ortogonali <i><img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image241.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="37" /></i>, e<img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image239.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="55" /> nel sistema di assi paralleli e concordi <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image242.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="46" />.<br />Se l'origine del nuovo sistema <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image242.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="46" /> ha, rispetto al primo, le coordinate <img alt="formula" class="img-middle" height="22" src="http://www.math.it/formulario/images/cambia_rif/Image240.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="54" />, valgono le relazioni:<br /><img alt="formula" height="48" src="http://www.math.it/formulario/images/cambia_rif/Image244.gif" width="75" /> .</span></td><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" valign="top" width="49%"><table border="0" cellpadding="3" cellspacing="3" style="line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
5. <tr align="center" valign="top"><td style="font-size: 0.9em;"><span style="color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
6. <tr align="right" valign="top"><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><span style="color: #0b5394;">Muovi il punto P in una posizone a tuo piacere, oppure il punto O' per effettuare una traslazione del sistema di riferimento XO'Y.</span></td></tr>
7. </tbody></table>
8. </td></tr>
9. <tr><td align="left" class="dividisotto" colspan="2" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" valign="top"><b><span style="color: #0b5394;">Formule per la rotazione degli assi</span></b><br />
10. <span style="color: #0b5394;">Le coordinate del generico punto P sono:<br /><img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image238.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="50" /> nel sistema di assi cartesiani ortogonali <i><img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image241.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="37" /></i>, e<img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image239.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="55" /> riferite al sistema <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image242.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="46" /> in cui gli assi sono ruotati di un angolo <span class="greco" style="font-family: Courier, Times, Arial, Helvetica, sans-serif; font-size: 1.6em; font-style: italic; letter-spacing: 0.2em;">α</span>, e le origini O e O' coincidono.</span><br />
11. <span style="color: #0b5394;">Le relazioni:<br /><img alt="formula" height="48" src="http://www.math.it/formulario/images/cambia_rif/Image245.gif" width="150" />,<br />consentono di passare da un sistema di riferimento <i><img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image241.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="37" /></i> al sistema <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image242.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="46" /> ruotato di un angolo <span class="greco" style="font-family: Courier, Times, Arial, Helvetica, sans-serif; font-size: 1.6em; font-style: italic; letter-spacing: 0.2em;">α</span>rispetto al precedente.</span><br />
12. <i><span style="color: #0b5394;">Disponendo per esempio dell'equazione cartesiana di una curva y=f(x) con queste formule si può trasformare l'equazione della curva nelle nuove variabili X,Y. Un esempio tipico è quello di trasformare l'equazione di un iperbole equilatera nell'equazione della stessa iperbole riferita ai propri asintoti.</span></i></td><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" valign="top" width="49%"><table border="0" cellpadding="3" cellspacing="3" style="line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
13. <tr align="center" valign="top"><td style="font-size: 0.9em;"><span style="color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
14. <tr align="right" valign="top"><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><span style="color: #0b5394;">I due riferimenti xOy e XO'Y hanno la stessa origine O=O'.<br />Puoi muovere dove vuoi il punto P. Per effettuare una rotazione del sistema di riferimento XO'Y prova a ruotare l'asse X in senso antiorario.</span></td></tr>
15. </tbody></table>
16. </td></tr>
17. <tr><td align="left" class="dividisotto" colspan="2" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" valign="top"><b><span style="color: #0b5394;">Formule per la rototraslazione degli assi</span></b><br />
18. <span style="color: #0b5394;">Questo movimento risulta composto dalla traslazione che porta dal sistema <i><img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image241.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="37" /></i> al sistema <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image243.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="51" /><br /><img alt="formula" height="48" src="http://www.math.it/formulario/images/cambia_rif/Image246.gif" width="79" />,<br />e dalla rotazione di un angolo <span class="greco" style="font-family: Courier, Times, Arial, Helvetica, sans-serif; font-size: 1.6em; font-style: italic; letter-spacing: 0.2em;">α</span> che porta dal sistema <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image243.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="51" /> al sistema <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image242.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="46" /><br /><img alt="formula" height="48" src="http://www.math.it/formulario/images/cambia_rif/Image247.gif" width="157" />.</span><br />
19. <span style="color: #0b5394;">Si ottengono così le formule per la rototraslazione:<br /><img alt="formula" class="img-middle" height="48" src="http://www.math.it/formulario/images/cambia_rif/Image248.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="173" /></span></td><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" valign="top" width="49%"><table border="0" cellpadding="3" cellspacing="3" style="line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
20. <tr align="center" valign="top"><td style="font-size: 0.9em;"><span style="color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
21. <tr align="right" valign="top"><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><span style="color: #0b5394;">I due riferimenti XO'Y e X'O'Y' hanno la stessa origine O'.<br />Muovi il punto P a tuo piacere. Per effettuare la traslazione del riferimento X'O'Y' trascina il punto O'. Per effettuare una traslazione del riferimento XO'Y ruota l'asse X in senso antiorario.</span></td></tr>
22. </tbody></table>
23. </td></tr>
24. <tr><td align="left" colspan="2" style="font-size: 0.9em;" valign="top"><b><span style="color: #0b5394;">Formule di trasformazione da coordinate cartesiane a coordinate polari e viceversa.</span></b><br />
25. <span style="color: #0b5394;">La posizione di un punto qualsiasi sul piano è univocamente determinata da:<br />- la sua distanza dal <i>polo</i> = <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">RAGGIO VETTORE</span><br />- l'angolo (<span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">ANOMALIA</span> o <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">ASCISSA ANGOLARE</span>) formato dall'<i>asse polare </i>e dal <i>raggio vettore</i>, assumendo l'<i>asse polare</i> come origine, e positivo il senso antiorario.</span><br />
26. <span style="color: #0b5394;">Per rappresentare tutti i punti del piano si conviene che:<br /><img alt="formula" class="img-middle" height="14" src="http://www.math.it/formulario/images/cambia_rif/Image249.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="30" />, <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image250.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="73" />.</span><br />
27. <span style="color: #0b5394;">Osservazioni:<br />- Tutti i punti dell'<i>asse polare</i> hanno <i>anomalia</i> nulla.<br />- L'equazione polare dell'<i>asse</i> é <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image251.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="39" />oppure <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image252.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="48" /><br />- Tutte le rette passanti per il <i>polo</i> hanno un'equazione del tipo:<img alt="formula" class="img-middle" height="19" src="http://www.math.it/formulario/images/cambia_rif/Image254.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="83" /><br />- Un cerchio con centro nel <i>polo</i> ha un'equazione del tipo:<img alt="formula" class="img-middle" height="19" src="http://www.math.it/formulario/images/cambia_rif/Image255.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="81" /><br />- Il <i>polo</i> ha <i>raggio vettore</i> nullo e <i>anomalia</i>indeterminata.</span><br />
28. <span style="color: #0b5394;">Per passare dal sistema cartesiano <i><img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/cambia_rif/Image241.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="37" /></i> al sistema polare (applicando il <a href="http://www.math.it/formulario/trigonometria.htm" style="text-decoration: none;">primo teorema sui triangoli rettangoli</a>) si usano le seguenti relazioni:<br /><img alt="formula" height="48" src="http://www.math.it/formulario/images/cambia_rif/Image256.gif" width="86" />,</span><br />
29. <span style="color: #0b5394;">Viceversa, per passare dal sistema polare al cartesiano:<br /><img alt="formula" class="img-middle" height="49" src="http://www.math.it/formulario/images/cambia_rif/Image257.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="118" />, <img alt="formula" class="img-middle" height="49" src="http://www.math.it/formulario/images/cambia_rif/Image258.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="118" />, <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/cambia_rif/Image259.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="57" />.</span></td></tr>
30. </tbody></table>
31. </div>
32. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/6566471091033386027/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-analitica-cambiamento-di.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/6566471091033386027'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/6566471091033386027'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-analitica-cambiamento-di.html' title='geometria analitica. Cambiamento di riferimento. Traslazione, rotazione, rototraslazione e coordinate polari'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-2478966505462074669</id><published>2016-03-13T16:45:00.003-07:00</published><updated>2016-03-13T16:47:45.459-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="geometria analitica"/><category scheme="http://www.blogger.com/atom/ns#" term="iperbole"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>iperbole</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
33. <table align="center" border="0" cellpadding="5" cellspacing="1" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
34. <tr><td class="divididestra" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;" valign="top"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
35. <b><span style="color: #0b5394;">Iperbole</span></b></div>
36. <span style="color: #0b5394;"><b>» </b>equazione cartesiana:<img alt="formula" class="img-middle" height="47" src="http://www.math.it/formulario/images/iperbole/equaz01.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="83" /></span><br />
37. <span style="color: #0b5394;"><b>» </b>fuochi: <img alt="formula" class="img-middle" height="28" src="http://www.math.it/formulario/images/iperbole/fuochi01.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="211" /></span><br />
38. <span style="color: #0b5394;"><b>» </b>asintoti: <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/iperbole/asintoti01a.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="64" /> , <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/iperbole/asintoti01b.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="52" /><br /><b>» </b>eccentricità: <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/iperbole/eccentric.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="40" /></span></td><td class="divididestra" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;" valign="top"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
39. <br /></div>
40. <span style="color: #0b5394;"><b>» </b>equazione cartesiana:<img alt="" class="img-middle" height="47" src="http://www.math.it/formulario/images/iperbole/equaz02.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="93" /></span><br />
41. <span style="color: #0b5394;"><b>» </b>fuochi: <img alt="formula" class="img-middle" height="28" src="http://www.math.it/formulario/images/iperbole/fuochi02.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="215" /></span><br />
42. <span style="color: #0b5394;"><b>» </b>asintoti: <img alt="" class="img-middle" height="41" src="http://www.math.it/formulario/images/iperbole/asintoti02a.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="64" /> , <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/iperbole/asintoti02b.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="52" /></span></td><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" valign="top"><span style="color: #0b5394;"><b>» </b><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Definizione</span>: l'<b>iperbole</b> è il luogo geometrico dei punti del piano per i quali è costante la differenza delle distanze da due punti fissi detti <b>fuochi</b>.</span><br />
43. <br />
44. <br />
45. <br />
46. <span style="color: #0b5394;"><b>» </b>Vista come sezione di un cono rotondo indefinito, l'iperbole è quella conica che si ottiene come sezione piana del cono di rotazione con un piano parallelo all'asse del cono.</span></td></tr>
47. <tr><td class="divididestra" colspan="2" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;" valign="top"><br />
48. <div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
49. <b><span style="color: #0b5394;">Iperbole equilatera riferita agli asintoti</span></b></div>
50. <span style="color: #0b5394;"><b>» </b>equazione cartesiana: <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/iperbole/equaz03.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="43" /><br /><b>» </b>lunghezza del semiasse trasverso: <img alt="formula" class="img-middle" height="31" src="http://www.math.it/formulario/images/iperbole/semia.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="65" /></span><br />
51. <span style="color: #0b5394;"><b>» </b>coordinate dei vertici sul semiasse trasverso:</span><br />
52. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="25" src="http://www.math.it/formulario/images/iperbole/vertici03.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="225" /></span><br />
53. <span style="color: #0b5394;"><b>» </b>coordinate dei fuochi:</span><br />
54. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="25" src="http://www.math.it/formulario/images/iperbole/fuochi03.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="260" /></span></td></tr>
55. </tbody></table>
56. </div>
57. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/2478966505462074669/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/iperbole.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/2478966505462074669'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/2478966505462074669'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/iperbole.html' title='iperbole'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-1109910420684550809</id><published>2016-03-13T16:44:00.006-07:00</published><updated>2016-03-13T16:47:45.455-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="ellisse"/><category scheme="http://www.blogger.com/atom/ns#" term="geometria analitica"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>ellisse</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
58. <table align="center" border="0" cellpadding="5" cellspacing="1" style="color: #660066; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
59. <tr><td class="divididestra" colspan="2" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;" valign="top"><span style="background-color: #0b5394;"><b>» </b>equazione cartesiana: <img alt="formula" class="img-middle" height="47" src="http://www.math.it/formulario/images/ellisse/equaz.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="83" /></span><br />
60. <span style="background-color: #0b5394;"><b>» </b>fuochi:<br /><img alt="formula" class="img-middle" height="28" src="http://www.math.it/formulario/images/ellisse/fuochi01.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="343" /><br /><img alt="formula" class="img-middle" height="28" src="http://www.math.it/formulario/images/ellisse/fuochi02.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="345" /></span><br />
61. <span style="background-color: #0b5394;"><b>» </b>vertici: <img alt="formula" class="img-middle" height="23" src="http://www.math.it/formulario/images/ellisse/vertici.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="245" /></span><br />
62. <span style="background-color: #0b5394;"><b>» </b>lunghezza asse maggiore = <img alt="2a" class="img-middle" height="19" src="http://www.math.it/formulario/images/ellisse/2a.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="21" /></span><br />
63. <span style="background-color: #0b5394;"><b>» </b>lunghezza asse minore = <img alt="2b" class="img-middle" height="19" src="http://www.math.it/formulario/images/ellisse/2b.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="21" /></span><br />
64. <span style="background-color: #0b5394;"><b>» </b>eccentricità : <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/ellisse/eccentric.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="40" /></span><br />
65. <span style="background-color: #0b5394;"><b>» </b> equazione della retta tangente all’ellisse nel suo punto <img alt="p con zero" class="img-middle" height="26" src="http://www.math.it/formulario/images/ellisse/pzero.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="70" />: <img alt="tangente in P0" class="img-middle" height="42" src="http://www.math.it/formulario/images/ellisse/tgp0.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="90" /></span><br />
66. <span style="background-color: #0b5394;"><b>» </b>Coefficienti angolari <i>m</i> delle rette tangenti all’ellisse condotte dal punto esterno <img alt="p con zero" class="img-middle" height="26" src="http://www.math.it/formulario/images/ellisse/pzero.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="70" />, sono le soluzioni dell’equazione : <img alt="coefficienti angolari" class="img-middle" height="32" src="http://www.math.it/formulario/images/ellisse/coeffang.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="241" /></span></td><td style="font-size: 0.9em;" valign="top"><span style="background-color: #0b5394;"><span class="evidenziato" style="font-weight: bold; letter-spacing: 0.1em;">Definizione</span>: l'<b><i>ellisse</i> </b>è il luogo geometrico dei punti del piano per i quali è costante (=<img alt="2a" class="img-middle" height="19" src="http://www.math.it/formulario/images/ellisse/2a.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="21" />) la somma delle distanze da due punti fissi detti <b><i>fuochi</i>.</b></span><br />
67. <br />
68. <br />
69. <br />
70. <br />
71. <span style="background-color: #0b5394;"><b>» </b>Vista come <b>sezione di un cono rotondo</b> indefinito, la ellisse è quella conica che si ottiene come sezione piana del cono di rotazione con un piano, non parallelo alla generatrice, e incidente l'asse del cono.</span></td></tr>
72. </tbody></table>
73. </div>
74. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/1109910420684550809/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/ellisse.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/1109910420684550809'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/1109910420684550809'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/ellisse.html' title='ellisse'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-6848024404334865370</id><published>2016-03-13T16:44:00.002-07:00</published><updated>2016-03-13T16:47:45.475-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="geometria analitica"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><category scheme="http://www.blogger.com/atom/ns#" term="parabola"/><title type='text'>parabola</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
75. <table align="center" border="0" cellpadding="5" cellspacing="1" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
76. <tr><td class="divididestra" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;" valign="top"><span style="color: #0b5394;"><b>» </b><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Definizione</span>: la <b>parabola</b> è il luogo geometrico dei punti del piano equidistante da un punto fisso, detto <b>fuoco</b>, e da una retta fissa, chiamata<b>direttrice</b>.</span></td><td class="divididestra" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;" valign="top"><span style="color: #0b5394;"><b>» </b>Vista come sezione di un cono rotondo indefinito, la parabola è quella conica che si ottiene come sezione piana del cono di rotazione con un piano parallelo alla generatrice del cono.</span></td></tr>
77. <tr><td class="divididestra" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;" valign="top" width="50%"><b><span style="color: #0b5394;">Parabola con asse verticale</span></b><br />
78. <span style="color: #0b5394;"><b>» </b>equazione cartesiana: <img alt="formula" class="img-middle" height="17" src="http://www.math.it/formulario/images/parabola/eq-parabola.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="98" /><br />vertice: <img alt="formula" class="img-middle" height="49" src="http://www.math.it/formulario/images/parabola/vertice.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="128" /><br /><b>» </b>fuoco: <img alt="formula" class="img-middle" height="49" src="http://www.math.it/formulario/images/parabola/fuoco.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="145" /><br /><b>» </b>asse: <img alt="formula" class="img-middle" height="40" src="http://www.math.it/formulario/images/parabola/asse.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="58" /><br /><b>» </b>direttrice: <img alt="formula" class="img-middle" height="42" src="http://www.math.it/formulario/images/parabola/direttrice.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="116" /></span></td><td class="divididestra" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;" valign="top" width="50%"><b><span style="color: #0b5394;">Parabola con asse orizzontale</span></b><br />
79. <span style="color: #0b5394;"><b>» </b>equazione cartesiana: <img alt="formula" class="img-middle" height="23" src="http://www.math.it/formulario/images/parabola/eq-parabolax.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="103" /><br /><b>» </b>vertice: <img alt="formula" class="img-middle" height="53" src="http://www.math.it/formulario/images/parabola/vertice2.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="129" /><br /><b>» </b>fuoco: <img alt="formula" class="img-middle" height="53" src="http://www.math.it/formulario/images/parabola/fuoco2.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="146" /><br /><b>» </b>asse: <img alt="formula" class="img-middle" height="40" src="http://www.math.it/formulario/images/parabola/assex.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="59" /><br /><b>» </b>direttrice: <img alt="formula" class="img-middle" height="42" src="http://www.math.it/formulario/images/parabola/direttricex.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="115" /></span></td></tr>
80. </tbody></table>
81. </div>
82. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/6848024404334865370/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/parabola.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/6848024404334865370'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/6848024404334865370'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/parabola.html' title='parabola'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-8463200627447309771</id><published>2016-03-13T16:43:00.003-07:00</published><updated>2016-03-13T16:47:45.479-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="circonferenza"/><category scheme="http://www.blogger.com/atom/ns#" term="geometria analitica"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>circonferenza</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
83. <table align="center" border="0" cellpadding="5" cellspacing="1" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
84. <tr><td align="left" class="divididestra" colspan="2" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;" valign="top"><span style="color: #0b5394;"><b>» </b>equazione della circonferenza di centro: <img alt="formula" class="img-middle" height="23" src="http://www.math.it/formulario/images/circonferenza/c.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="51" /> e raggio <i>r</i>: <img alt="formula" class="img-middle" height="27" src="http://www.math.it/formulario/images/circonferenza/equaz2.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="151" /></span><br />
85. <span style="color: #0b5394;"><b>» </b>equazione cartesiana (equazione canonica): <img alt="formula" class="img-middle" height="25" src="http://www.math.it/formulario/images/circonferenza/equaz.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="303" /><br /><b>» </b>centro: <img alt="formula" class="img-middle" height="23" src="http://www.math.it/formulario/images/circonferenza/c.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="51" /><br /><b>» </b>raggio: <img alt="formula" class="img-middle" height="28" src="http://www.math.it/formulario/images/circonferenza/raggio.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="231" /><br /><b>» </b>condizione di realtà: <img alt="formula" class="img-middle" height="23" src="http://www.math.it/formulario/images/circonferenza/condizione.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="101" /><br /><b>» </b>asse radicale di due circonferenze <img alt="circonferenza" class="img-middle" height="26" src="http://www.math.it/formulario/images/circonferenza/circ1.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="176" /> e <img alt="circonferenza" class="img-middle" height="28" src="http://www.math.it/formulario/images/circonferenza/circ2.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="190" />: <img alt="asse radicale" class="img-middle" height="26" src="http://www.math.it/formulario/images/circonferenza/asseradicale.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="209" /></span><br />
86. <table align="center" border="0" cellpadding="3" cellspacing="3" class="cornice" style="border: 1px solid rgb(238, 238, 238); line-height: 1.2em; margin: 0px; padding: 5px;"><tbody>
87. <tr><td style="font-size: 0.9em;"><span style="color: #0b5394;">L'<b>asse radicale</b> di due circonferenza è la retta che passa per i loro punti di intersezione.</span></td></tr>
88. <tr><td style="font-size: 0.9em;"><div id="applet_container" style="display: inline; height: 400px; width: 500px;">
89. <div class="applet_scaler" style="height: 400px; position: relative; transform-origin: 0% 0% 0px; transform: none; width: 500px;">
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91. <tr><td align="left" style="font-size: 0.9em; vertical-align: top;"><div style="height: 398px; position: relative; width: 498px;">
92. <span style="color: #0b5394;"><div aria-hidden="true" style="height: 10ex; position: absolute; top: -20ex; visibility: hidden; width: 10em; z-index: -32767;">
93. </div>
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98. </div>
99. </div>
100. </span></div>
101. </td></tr>
102. </tbody></table>
103. </article></div>
104. </div>
105. </td></tr>
106. <tr><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><span style="color: #0b5394;">Puoi variare la posizione dei centri delle due circonferenze o il loro raggio. Cosa succede all'asse radicale quando le due circonferenze non si intersecano?</span></td></tr>
107. </tbody></table>
108. </td><td align="left" style="font-size: 0.9em;" valign="top" width="49%"><span style="color: #0b5394;"><b>» </b><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Definizione</span>: la <b>circonferenza </b>è il luogo geometrico dei punti del piano equidistante da un punto fisso, detto<b>centro.</b></span><br />
109. <div class="dividisopra" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px;">
110. <span style="color: #0b5394;"><b>» </b> Vista come sezione di un cono rotondo indefinito, la circonferenza è quella conica che si ottiene come sezione piana del cono di rotazione con un piano perpendicolare all'asse del cono.</span></div>
111. </td></tr>
112. </tbody></table>
113. </div>
114. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/8463200627447309771/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/circonferenza.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/8463200627447309771'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/8463200627447309771'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/circonferenza.html' title='circonferenza'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-5461514316305308882</id><published>2016-03-13T16:42:00.003-07:00</published><updated>2016-03-13T16:47:45.467-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="geometria analitica"/><category scheme="http://www.blogger.com/atom/ns#" term="la retta"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>la retta</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
115. <table align="center" border="0" cellpadding="5" cellspacing="1" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
116. <tr><td class="divididestra" colspan="2" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;" valign="top"><span style="color: #0b5394;"><b>» </b>equazione cartesiana in <b>forma implicita</b>: <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/retta/Image320.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="98" /><br /><b>» </b>coeffciente angolare: <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/retta/Image345.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="123" /><br /><b>» </b>termine noto: <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/retta/Image346.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="119" /></span><br />
117. <span style="color: #0b5394;"><b>» </b>Condizione di parallelismo tra le due rette <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/retta/Image320.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="98" /> e <img alt="formula" class="img-middle" height="22" src="http://www.math.it/formulario/images/retta/Image331.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="115" />:<br /><img alt="formula" class="img-middle" height="22" src="http://www.math.it/formulario/images/retta/Image332.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="91" /></span><br />
118. <span style="color: #0b5394;"><b>» </b>Condizione di perpendicolarità tra le due rette <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/retta/Image320.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="98" /> e <img alt="formula" class="img-middle" height="22" src="http://www.math.it/formulario/images/retta/Image331.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="115" />:<br /><img alt="formula" class="img-middle" height="22" src="http://www.math.it/formulario/images/retta/Image333.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="91" /></span><br />
119. </td><td bgcolor="#FFFFFF" style="font-size: 0.9em;" valign="top" width="50%"><span style="color: #0b5394;"><b>» </b>equazione cartesiana in <b>forma esplicita</b>: <img alt="formula" class="img-middle" height="18" src="http://www.math.it/formulario/images/retta/Image321.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="73" /></span><br />
120. <span style="color: #0b5394;"><b>» </b>coefficiente angolare: <img alt="formula" class="img-middle" height="46" src="http://www.math.it/formulario/images/retta/Image322.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="162" /></span><br />
121. <span style="color: #0b5394;"><b>» </b>termine noto o intercetta: <img alt="formula" class="img-middle" height="46" src="http://www.math.it/formulario/images/retta/Image323.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="182" /></span><br />
122. <span style="color: #0b5394;"><b>» </b>equazione della retta passante per due punti <img alt="formula" class="img-middle" height="23" src="http://www.math.it/formulario/images/retta/Image342.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="63" />, <img alt="formula" class="img-middle" height="23" src="http://www.math.it/formulario/images/retta/Image343.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="69" />:<br /><img alt="formula" class="img-middle" height="46" src="http://www.math.it/formulario/images/retta/Image324.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="273" /><br /><img alt="formula" class="img-middle" height="22" src="http://www.math.it/formulario/images/retta/Image325.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="133" /><br /><img alt="formula" class="img-middle" height="22" src="http://www.math.it/formulario/images/retta/Image326.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="137" /></span><br />
123. <span style="color: #0b5394;"><b>» </b>equazione della retta passante per un punto <img alt="formula" class="img-middle" height="24" src="http://www.math.it/formulario/images/retta/Image341.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="69" />:<br /><img alt="formula" class="img-middle" height="24" src="http://www.math.it/formulario/images/retta/Image340.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="125" /> (fascio di rette proprio)</span><br />
124. <span style="color: #0b5394;"><b>» </b>condizione di parallelismo tra le due rette <img alt="formula" class="img-middle" height="18" src="http://www.math.it/formulario/images/retta/Image321.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="73" />, <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/retta/Image327.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="81" />: <img alt="formula" class="img-middle" height="18" src="http://www.math.it/formulario/images/retta/Image328.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="48" /></span><br />
125. <span style="color: #0b5394;"><b>» </b>condizione di perpendicolarità tra le due rette <img alt="formula" class="img-middle" height="18" src="http://www.math.it/formulario/images/retta/Image321.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="73" />, <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/retta/Image327.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="81" />:<br /><img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/retta/Image329.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="61" /> o anche <img alt="formula" class="img-middle" height="18" src="http://www.math.it/formulario/images/retta/Image330.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="70" /></span><br />
126. <span style="color: #0b5394;"><b>» </b>angolo tra due rette <img alt="formula" class="img-middle" height="18" src="http://www.math.it/formulario/images/retta/Image321.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="73" />, <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/retta/Image327.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="81" />:<br /><img alt="formula" class="img-middle" height="45" src="http://www.math.it/formulario/images/retta/Image347.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="107" /></span></td></tr>
127. </tbody></table>
128. </div>
129. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/5461514316305308882/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/la-retta.html#comment-form' title='1 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/5461514316305308882'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/5461514316305308882'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/la-retta.html' title='la retta'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-3278213084175956685</id><published>2016-03-13T16:42:00.000-07:00</published><updated>2016-03-13T16:47:45.463-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="geometria analitica"/><category scheme="http://www.blogger.com/atom/ns#" term="geometria analitica - metrica"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>geometria analitica - metrica</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
130. <table border="0" cellpadding="0" cellspacing="0" style="color: #660066; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px;"><tbody>
131. <tr><td colspan="2" style="font-size: 0.9em;"><img alt="formula" height="22" src="http://www.math.it/formulario/images/metrici/Image461.gif" width="61" />, <img alt="formula" height="22" src="http://www.math.it/formulario/images/metrici/Image462.gif" width="63" />, <img alt="formula" height="23" src="http://www.math.it/formulario/images/metrici/Image463.gif" width="62" /><br />
132. <b>» </b>Coordinate del punto medio di un segmento:<br />
133. <img alt="formula" height="42" src="http://www.math.it/formulario/images/metrici/Image464.gif" width="91" /> , <img alt="formula" height="42" src="http://www.math.it/formulario/images/metrici/Image465.gif" width="94" /><br />
134. <b>» </b>Distanza tra due punti:<br />
135. <img alt="formula" height="30" src="http://www.math.it/formulario/images/metrici/Image466.gif" width="198" /><br />
136. <b>» </b>Distanza di un punto da una retta di equazione <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/metrici/Image467.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="98" />:<br />
137. <img alt="formula" height="51" src="http://www.math.it/formulario/images/metrici/Image468.gif" width="118" /><br />
138. <table border="0" cellpadding="3" cellspacing="3" class="cornice" style="border: 1px solid rgb(238, 238, 238); line-height: 1.2em; margin: 0px; padding: 5px;"><tbody>
139. <tr><td style="font-size: 0.9em;"><div id="applet_container1" style="display: inline; height: 260px; width: 400px;">
140. <div class="applet_scaler" style="height: 260px; position: relative; transform-origin: 0% 0% 0px; transform: none; width: 400px;">
141. <article class="notranslate geogebraweb" data-param-enablelabeldrags="false" data-param-enablerightclick="false" data-param-enableshiftdragzoom="true" data-param-errordialogsactive="true" data-param-ggbbase64="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" data-param-height="260" data-param-showalgebrainput="false" data-param-showmenubar="false" data-param-showreseticon="false" data-param-showsplash="false" data-param-showtoolbar="false" data-param-showtoolbarhelp="false" data-param-usebrowserforjs="false" data-param-width="400" data-scalex="1" data-scaley="1" id="geogebraweb01457912500949" style="-webkit-tap-highlight-color: rgba(255, 255, 255, 0); border: 0px solid rgb(211, 211, 211); display: inline-block;"><table cellpadding="0" cellspacing="0" class="GeoGebraFrame jsloaded" style="border: 1px solid rgb(211, 211, 211); font-family: geogebra-sans-serif, Frutiger, 'Frutiger Linotype', Univers, Calibri, 'Gill Sans', 'Gill Sans MT', 'Myriad Pro', Myriad, 'DejaVu Sans Condensed', 'Liberation Sans', 'Nimbus Sans L', Tahoma, Geneva, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 15.552px; font-stretch: normal; height: auto; line-height: 1.2em; margin: 0px; padding: 5px; position: relative; width: auto;"><tbody>
142. <tr><td align="left" style="font-size: 0.9em; vertical-align: top;"><div style="height: 258px; position: relative; width: 398px;">
143. <div aria-hidden="true" style="height: 10ex; position: absolute; top: -20ex; visibility: hidden; width: 10em; z-index: -32767;">
144. </div>
145. <div style="bottom: 0px; left: 0px; overflow: hidden; position: absolute; right: 0px; top: 0px;">
146. <div style="bottom: 0px; left: 0px; position: absolute; right: 0px; top: 0px;">
147. <div class="EuclidianPanel" dir="ltr" style="bottom: -1px; height: 258px; left: 0px; overflow: hidden; position: relative; right: -1px; top: 0px; width: 398px;">
148. <canvas dir="ltr" height="258" id="View_1" style="-webkit-user-select: none; height: 258px; position: absolute; width: 398px; z-index: 0;" tabindex="0" width="398"></canvas></div>
149. </div>
150. </div>
151. </div>
152. </td></tr>
153. </tbody></table>
154. </article></div>
155. </div>
156. </td></tr>
157. <tr><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;">Muovi il punto P o la retta r per vedere come varia la distanza PH tra il punto e la retta.</td></tr>
158. </tbody></table>
159. <b>» </b>Distanza di un punto da una retta di equazione <img alt="formula" class="img-middle" height="18" src="http://www.math.it/formulario/images/metrici/Image469.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="73" /><br />
160. <img align="middle" alt="formula" height="51" src="http://www.math.it/formulario/images/metrici/Image470.gif" width="126" /><br />
161. <b>» </b>angolo tra due rette <img alt="formula" class="img-middle" height="18" src="http://www.math.it/formulario/images/retta/Image321.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="73" />, <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/retta/Image327.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="81" />:<br /><img alt="formula" class="img-middle" height="45" src="http://www.math.it/formulario/images/retta/Image347.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="107" /></td><td style="font-size: 0.9em;" valign="top" width="49%"><table border="0" cellpadding="3" cellspacing="3" class="cornice" style="border: 1px solid rgb(238, 238, 238); line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
162. <tr><td style="font-size: 0.9em;"><div id="applet_container2" style="display: inline; height: 260px; width: 329px;">
163. <div class="applet_scaler" style="height: 260px; position: relative; transform-origin: 0% 0% 0px; transform: none; width: 329px;">
164. <article class="notranslate geogebraweb" data-param-enablelabeldrags="false" data-param-enablerightclick="false" data-param-enableshiftdragzoom="true" data-param-errordialogsactive="true" data-param-ggbbase64="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" data-param-height="260" data-param-showalgebrainput="false" data-param-showmenubar="false" data-param-showreseticon="false" data-param-showsplash="false" data-param-showtoolbar="false" data-param-showtoolbarhelp="false" data-param-usebrowserforjs="false" data-param-width="329" data-scalex="1" data-scaley="1" id="geogebraweb11457912500951" style="-webkit-tap-highlight-color: rgba(255, 255, 255, 0); border: 0px solid rgb(211, 211, 211); display: inline-block;"><table cellpadding="0" cellspacing="0" class="GeoGebraFrame jsloaded" style="border: 1px solid rgb(211, 211, 211); font-family: geogebra-sans-serif, Frutiger, 'Frutiger Linotype', Univers, Calibri, 'Gill Sans', 'Gill Sans MT', 'Myriad Pro', Myriad, 'DejaVu Sans Condensed', 'Liberation Sans', 'Nimbus Sans L', Tahoma, Geneva, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 15.552px; font-stretch: normal; height: auto; line-height: 1.2em; margin: 0px; padding: 5px; position: relative; width: auto;"><tbody>
165. <tr><td align="left" style="font-size: 0.9em; vertical-align: top;"><div style="height: 258px; position: relative; width: 327px;">
166. <div aria-hidden="true" style="height: 10ex; position: absolute; top: -20ex; visibility: hidden; width: 10em; z-index: -32767;">
167. </div>
168. <div style="bottom: 0px; left: 0px; overflow: hidden; position: absolute; right: 0px; top: 0px;">
169. <div style="bottom: 0px; left: 0px; position: absolute; right: 0px; top: 0px;">
170. <div class="EuclidianPanel" dir="ltr" style="bottom: -1px; height: 258px; left: 0px; overflow: hidden; position: relative; right: -1px; top: 0px; width: 327px;">
171. <canvas dir="ltr" height="258" id="View_1" style="-webkit-user-select: none; height: 258px; position: absolute; width: 327px; z-index: 0;" tabindex="0" width="327"></canvas></div>
172. </div>
173. </div>
174. </div>
175. </td></tr>
176. </tbody></table>
177. </article></div>
178. </div>
179. </td></tr>
180. <tr><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;">Muovi il punto P per vedere come variano i suoi simmetrici ripetto agli assi e rispetto all'origine.</td></tr>
181. <tr><td class="more" style="background-image: url("../images/back_math-g.gif"); color: #777777; font-size: 0.9em; letter-spacing: 0.1em; line-height: 1.2em;">Nella sezione <i>costruzioni geometriche con Cabri</i> puoi imparare qualcos'altro sulla<b>simmetria</b> <a class="C" href="http://www.math.it/cabri/simm_assiale.htm" style="color: #ff6600; text-decoration: none;">assiale</a> e <a class="C" href="http://www.math.it/cabri/simm_centrale.htm" style="color: #ff6600; text-decoration: none;">centrale</a></td></tr>
182. </tbody></table>
183. <b>» </b>Coordinate del <a class="C" href="http://www.math.it/cabri/baricentro.htm" style="color: #ff6600; text-decoration: none;">baricentro del triangolo</a> <i>ABC </i>(note le coordinate dei tre punti):<br />
184. <img alt="formula" class="img-middle" height="42" src="http://www.math.it/formulario/images/metrici/Image471.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="118" />, <img alt="formula" class="img-middle" height="42" src="http://www.math.it/formulario/images/metrici/Image472.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="122" /><br />
185. <b>» </b>Area del triangolo <i>ABC</i><br />
186. Note le coordinate dei tre vertici A(x<sub>1</sub>;y<sub>1</sub>), B(x<sub>2</sub>;y<sub>2</sub>), C(x<sub>3</sub>;y<sub>3</sub>), l’Area si calcola con il determinante:<br /><img alt="formula" class="img-middle" height="74" src="http://www.math.it/formulario/images/triangolo/Image658.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="149" /> , <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/metrici/Image473.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="62" />,<br />dove <img alt="formula" class="img-middle" height="58" src="http://www.math.it/formulario/images/metrici/Image474.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="145" />, ovvero <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/metrici/Image475.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="286" /></td></tr>
187. </tbody></table>
188. </div>
189. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/3278213084175956685/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-analitica-metrica.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/3278213084175956685'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/3278213084175956685'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-analitica-metrica.html' title='geometria analitica - metrica'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-1179223676050178575</id><published>2016-03-13T16:41:00.000-07:00</published><updated>2016-03-13T16:41:24.792-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="geometria analitica"/><category scheme="http://www.blogger.com/atom/ns#" term="Trasformazioni geometriche"/><title type='text'>Trasformazioni geometriche</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
190. <table align="center" border="0" cellpadding="5" cellspacing="1" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
191. <tr><td align="left" class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" valign="top"><span style="color: #0b5394;"><b>Traslazione</b> di vettore <img alt="formula" class="img-middle" height="28" src="http://www.math.it/formulario/images/trasformaz_geometriche/image001.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="61" /></span><br />
192. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="50" src="http://www.math.it/formulario/images/trasformaz_geometriche/image004.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="81" /></span><br />
193. <span style="color: #0b5394;"><b>Rotazione</b> di un angolo <span class="greco" style="font-family: Courier, Times, Arial, Helvetica, sans-serif; font-size: 1.6em; font-style: italic; letter-spacing: 0.2em;">α</span></span><br />
194. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="48" src="http://www.math.it/formulario/images/trasformaz_geometriche/image024.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="146" /></span><br />
195. <span style="color: #0b5394;"><b>Simmetria centrale</b> di centro C <img alt="formula" class="img-middle" height="26" src="http://www.math.it/formulario/images/trasformaz_geometriche/image006.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="50" /></span><br />
196. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="50" src="http://www.math.it/formulario/images/trasformaz_geometriche/image007.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="89" /></span><br />
197. <b><span style="color: #0b5394;">Simmetria assiale</span></b><br />
198. <span style="color: #0b5394;">Rispetto all’asse delle ascisse (<img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/trasformaz_geometriche/image009.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="37" />)<br /><img alt="formula" class="img-middle" height="48" src="http://www.math.it/formulario/images/trasformaz_geometriche/image010.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="61" /></span><br />
199. <span style="color: #0b5394;">Rispetto all’asse delle ordinate (<img alt="formula" class="img-middle" height="18" src="http://www.math.it/formulario/images/trasformaz_geometriche/image011.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="37" />)</span><br />
200. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="48" src="http://www.math.it/formulario/images/trasformaz_geometriche/image012.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="58" /></span><br />
201. <span style="color: #0b5394;">Rispetto ad una retta parallela all’asse delle ascisse (<img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/trasformaz_geometriche/image013.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="38" />)</span><br />
202. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="48" src="http://www.math.it/formulario/images/trasformaz_geometriche/image014.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="92" /></span><br />
203. <span style="color: #0b5394;">Rispetto ad una retta parallela all’asse delle ordinate (<img alt="formula" class="img-middle" height="18" src="http://www.math.it/formulario/images/trasformaz_geometriche/image015.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="37" />)</span><br />
204. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="48" src="http://www.math.it/formulario/images/trasformaz_geometriche/image016.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="90" /></span><br />
205. <span style="color: #0b5394;">Rispetto alla bisettrice I, III (<img alt="formula" class="img-middle" height="17" src="http://www.math.it/formulario/images/trasformaz_geometriche/image017.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="38" />)</span><br />
206. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="48" src="http://www.math.it/formulario/images/trasformaz_geometriche/image018.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="50" /></span><br />
207. <span style="color: #0b5394;">Rispetto alla bisettrice II, IV (<img alt="formula" class="img-middle" height="17" src="http://www.math.it/formulario/images/trasformaz_geometriche/image019.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="48" />)</span><br />
208. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="48" src="http://www.math.it/formulario/images/trasformaz_geometriche/image020.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="60" /></span><br />
209. </td><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" valign="top" width="49%"><span style="color: #0b5394;"><b>Omotetia</b> di centro O(0,0) e rapporto <i>k</i></span><br />
210. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="48" src="http://www.math.it/formulario/images/trasformaz_geometriche/image021.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="62" /></span><br />
211. <span style="color: #0b5394;"><b>Omotetia</b> di centro O(0,0) rapporto <i>k</i> con traslazione di vettore <img alt="formula" class="img-middle" height="28" src="http://www.math.it/formulario/images/trasformaz_geometriche/image001.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="61" /></span><br />
212. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="50" src="http://www.math.it/formulario/images/trasformaz_geometriche/image022.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="92" /></span><br />
213. <span style="color: #0b5394;"><b>Omotetia</b> di centro C(<i>a</i>,<i>b</i>) e rapporto <i>k</i></span><br />
214. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="53" src="http://www.math.it/formulario/images/trasformaz_geometriche/image023.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="126" /></span></td></tr>
215. </tbody></table>
216. </div>
217. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/1179223676050178575/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/trasformazioni-geometriche.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/1179223676050178575'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/1179223676050178575'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/trasformazioni-geometriche.html' title='Trasformazioni geometriche'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-6436356933850006430</id><published>2016-03-13T16:38:00.003-07:00</published><updated>2016-03-13T16:39:27.464-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Geometria dello spazio"/><category scheme="http://www.blogger.com/atom/ns#" term="Geometria Solida. Parti della sfera e della superficie sferica"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>Geometria Solida. Parti della sfera e della superficie sferica</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
218. <span style="color: #0b5394;"><br /></span>
219. <table border="0" cellpadding="1" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
220. <tr><td style="font-size: 0.9em;" width="28%"><span style="color: #0b5394;"> </span></td><th style="background-color: #660066; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;" width="36%"><b><span style="color: #0b5394;">superficie</span></b></th><th style="background-color: #660066; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;" width="36%"><b><span style="color: #0b5394;">volume</span></b></th></tr>
221. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="28%"><b><span style="color: #0b5394;">Calotta sferica</span></b></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="36%"><span style="color: #0b5394;"><img alt="formula" height="29" src="http://www.math.it/formulario/images/poliedri/rotondi/Image518.gif" width="117" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="36%"><div align="center">
222. <br /></div>
223. </td></tr>
224. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="28%"><b><span style="color: #0b5394;">Zona sferica</span></b></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="36%"><span style="color: #0b5394;"><img alt="formula" height="29" src="http://www.math.it/formulario/images/poliedri/rotondi/Image519.gif" width="103" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="36%"><div align="center">
225. <br /></div>
226. </td></tr>
227. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="28%"><b><span style="color: #0b5394;">Fuso sferico</span></b></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="36%"><span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poliedri/rotondi/Image521.gif" width="106" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="36%"><div align="center">
228. <br /></div>
229. </td></tr>
230. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Segmento sferico a una base</span></b></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="45" src="http://www.math.it/formulario/images/poliedri/rotondi/Image522.gif" width="111" /></span></td></tr>
231. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Segmento sferico a due basi</span></b></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poliedri/rotondi/Image523.gif" width="159" /></span></td></tr>
232. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Spicchio sferico</span></b></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poliedri/rotondi/Image524.gif" width="75" /></span></td></tr>
233. </tbody></table>
234. <span style="color: #0b5394;"><br style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 23.04px;" /></span>
235. <table border="0" cellpadding="1" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
236. <tr valign="top"><td class="dividisoprasotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;" valign="top" width="65%"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
237. <b><span style="color: #0b5394;">Calotta sferica</span></b></div>
238. <span style="color: #0b5394;">L’area della <b>superficie della calotta sferica </b>è data dal prodotto della lunghezza della circonferenza massima della superficie a cui appartiene per la sua altezza:</span><br />
239. <span style="color: #0b5394;"><img alt="" height="29" src="http://www.math.it/formulario/images/poliedri/rotondi/Image518.gif" width="117" /></span></td><td align="center" class="dividisoprasotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;" width="35%"><span style="color: #0b5394;"><img alt="Calotta sferica" height="177" src="http://www.math.it/formulario/images/poliedri/rotondi/calotta.gif" width="177" /></span></td></tr>
240. <tr valign="top"><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" valign="top"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
241. <b><span style="color: #0b5394;">Zona sferica</span></b></div>
242. <span style="color: #0b5394;">L’area della <b>zona sferica</b> è data dal prodotto della lunghezza della circonferenza massima della superficie sferica a cui appartiene per la sua altezza:</span><br />
243. <span style="color: #0b5394;"><img alt="formula" height="29" src="http://www.math.it/formulario/images/poliedri/rotondi/Image519.gif" width="103" /></span></td><td align="center" class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><br />
244. <span style="color: #0b5394;"><img alt="Zona sferica" height="174" src="http://www.math.it/formulario/images/poliedri/rotondi/zona.gif" width="174" /></span></td></tr>
245. <tr valign="top"><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" valign="top"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
246. <b><span style="color: #0b5394;">Fuso sferico</span></b></div>
247. <span style="color: #0b5394;">È la parte di superficie sferica compresa tra due semipiani uscenti dallo stesso diametro. L’<i>ampiezza del fuso</i> è l’angolo <img alt="alfa" class="img-middle" height="14" src="http://www.math.it/formulario/images/poliedri/rotondi/Image520.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="16" />compreso tra i due semipiani.</span><br />
248. <span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poliedri/rotondi/Image521.gif" width="106" /></span></td><td align="center" class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><img alt="Fuso sferico" height="163" src="http://www.math.it/formulario/images/poliedri/rotondi/fuso.gif" width="132" /></span></td></tr>
249. <tr valign="top"><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" valign="top"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
250. <b><span style="color: #0b5394;">Segmento sferico a una base</span></b></div>
251. <span style="color: #0b5394;"><img alt="formula" height="45" src="http://www.math.it/formulario/images/poliedri/rotondi/Image522.gif" width="111" /></span></td><td align="center" class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><img alt="Segmento sferico a una base" height="175" src="http://www.math.it/formulario/images/poliedri/rotondi/segmentosferico1.gif" width="175" /></span></td></tr>
252. <tr valign="top"><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" valign="top"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
253. <b><span style="color: #0b5394;">Segmento sferico a due basi</span></b></div>
254. <span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poliedri/rotondi/Image523.gif" width="159" /></span></td><td align="center" class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><img alt="Segmento sferico a due basi" height="177" src="http://www.math.it/formulario/images/poliedri/rotondi/segmentosferico2.gif" width="177" /></span></td></tr>
255. <tr valign="top"><td style="font-size: 0.9em;" valign="top"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
256. <b><span style="color: #0b5394;">Spicchio sferico</span></b></div>
257. <span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poliedri/rotondi/Image524.gif" width="75" /></span></td><td align="center" style="font-size: 0.9em;"><span style="color: #0b5394;"><img alt="Spicchio sferico" height="169" src="http://www.math.it/formulario/images/poliedri/rotondi/spicchio.gif" width="139" /></span></td></tr>
258. </tbody></table>
259. </div>
260. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/6436356933850006430/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-solida-parti-della-sfera-e.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/6436356933850006430'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/6436356933850006430'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-solida-parti-della-sfera-e.html' title='Geometria Solida. Parti della sfera e della superficie sferica'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-545663170230027516</id><published>2016-03-13T16:37:00.002-07:00</published><updated>2016-03-13T16:39:27.460-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="cono"/><category scheme="http://www.blogger.com/atom/ns#" term="Geometria dello spazio"/><category scheme="http://www.blogger.com/atom/ns#" term="Geometria Solida. Solidi di rotazione. Cilindro"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><category scheme="http://www.blogger.com/atom/ns#" term="sfera"/><category scheme="http://www.blogger.com/atom/ns#" term="tronco di cono"/><title type='text'>Geometria Solida. Solidi di rotazione. Cilindro, cono, tronco di cono, sfera</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
261. <div style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 23.04px;">
262. <span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;"><b>Solidi di rotazione</b></span><br />Sono solidi ottenuti dalla rotazione di una figura piana intorno ad una retta (<i>asse di rotazione</i>).</span></div>
263. <table border="0" cellpadding="1" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
264. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="27%"></td><th style="background-color: #660066; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;" width="19%"><div align="center">
265. <b><span style="color: #0b5394;">superficie laterale</span></b></div>
266. </th><th style="background-color: #660066; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;" width="19%"><div align="center">
267. <b><span style="color: #0b5394;">superficie totale</span></b></div>
268. </th><th style="background-color: #660066; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;" width="13%"><div align="center">
269. <b><span style="color: #0b5394;">volume</span></b></div>
270. </th></tr>
271. <tr><td align="left" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="27%"><b><span style="color: #0b5394;">Cilindro</span></b></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="19%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/rotondi/Image506.gif" width="75" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="19%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/rotondi/Image507.gif" width="90" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="13%"><span style="color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/poliedri/rotondi/Image508.gif" width="72" /></span></td></tr>
272. <tr><td align="left" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="27%"><b><span style="color: #0b5394;">Cono</span></b></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="19%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/rotondi/Image509.gif" width="67" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="19%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/rotondi/Image510.gif" width="77" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="13%"><span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poliedri/rotondi/Image511.gif" width="74" /></span></td></tr>
273. <tr><td align="left" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="27%"><b><span style="color: #0b5394;">Tronco di cono</span></b></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="19%"><span style="color: #0b5394;"><img alt="formula" height="26" src="http://www.math.it/formulario/images/poliedri/rotondi/Image512.gif" width="109" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="19%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/rotondi/Image513.gif" width="113" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="13%"><span style="color: #0b5394;"><img alt="formula" height="52" src="http://www.math.it/formulario/images/poliedri/rotondi/Image514.gif" width="188" /></span></td></tr>
274. <tr><td align="left" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="27%"></td><th colspan="2" style="background-color: #660066; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><div align="center">
275. <b><span style="color: #0b5394;">superficie sferica</span></b></div>
276. </th><th style="background-color: #660066; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;" width="13%"><div align="center">
277. <b><span style="color: #0b5394;">volume</span></b></div>
278. </th></tr>
279. <tr><td align="left" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Sfera</span></b></td><td align="center" class="cornice" colspan="2" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/poliedri/rotondi/Image515.gif" width="61" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poliedri/rotondi/Image517.gif" width="66" /></span></td></tr>
280. </tbody></table>
281. <span style="color: #0b5394;"><br style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 23.04px;" /></span>
282. <table border="0" cellpadding="1" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
283. <tr><td class="dividisoprasotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;" valign="top" width="71%"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
284. <b><span style="color: #0b5394;">Cilindro</span></b></div>
285. <span style="color: #0b5394;"><b></b>Il <b>cilindro</b> è un solido ottenuto dalla rotazione completa di un rettangolo intorno ad un suo lato.</span><br />
286. <span style="color: #0b5394;"><b>Cilindro equilatero</b>È un cilindro in cui l’altezza è lunga quanto il diametro della base.</span><br />
287. <span style="color: #0b5394;">L’area della <b>superficie laterale</b> di un cilindro si ottiene moltiplicando la lunghezza della circonferenza di base per la misura dell’altezza:<br /><img alt="formula" class="img-middle" height="24" src="http://www.math.it/formulario/images/poliedri/rotondi/Image506.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="76" /></span><br />
288. <span style="color: #0b5394;">L’area della <b>superficie totale</b> di un cilindro si ottiene sommando la superficie laterale e l’area delle due basi:<br /><img alt="formula" class="img-middle" height="24" src="http://www.math.it/formulario/images/poliedri/rotondi/Image507.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="90" /></span><br />
289. <span style="color: #0b5394;">Il <b>volume</b> di un cilindro si ottiene moltiplicando l’area di base per la misura dell’altezza:<br /><img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/poliedri/rotondi/Image508.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="72" /></span></td><td align="center" class="dividisoprasotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;" width="29%"><span style="color: #0b5394;"><img alt="cilindro" height="202" src="http://www.math.it/formulario/images/poliedri/rotondi/cilindro.gif" width="158" /></span></td></tr>
290. <tr><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" valign="top"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
291. <b><span style="color: #0b5394;">Cono</span></b></div>
292. <span style="color: #0b5394;"><b></b>Il <b>cono</b> è un solido ottenuto dalla rotazione di un triangolo intorno ad un suo cateto.</span><br />
293. <span style="color: #0b5394;"><b>Cono equilatero</b>È un cono in cui l’apotema è lungo quanto il diametro della base.</span><br />
294. <span style="color: #0b5394;">L’area della <b>superficie laterale</b> di un cono si ottiene moltiplicando la lunghezza della circonferenza di base per la misura dell’apotema e dividendo tale prodotto per due:<br /><img alt="formula" class="img-middle" height="24" src="http://www.math.it/formulario/images/poliedri/rotondi/Image509.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="68" />, dove l’apotema è la lunghezza del lato obliquo del cono <img alt="formula" class="img-middle" height="28" src="http://www.math.it/formulario/images/poliedri/rotondi/Image527.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="86" /> .</span><br />
295. <span style="color: #0b5394;">L’area della <b>superficie totale</b> di un cono si ottiene sommando la superficie laterale e l’area della base:<br /><img alt="formula" class="img-middle" height="24" src="http://www.math.it/formulario/images/poliedri/rotondi/Image510.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="77" /></span><br />
296. <span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Proprietà</span>. Il cono è equivalente a un terzo di un cilindro avente base ed altezza congruenti rispettivamente alla base e all’altezza del cono.</span><br />
297. <span style="color: #0b5394;">Il <b>volume</b> di un cono si ottiene moltiplicando l’area di base per la misura dell’altezza e dividendo tale prodotto per tre:<br /><img alt="formula" class="img-middle" height="43" src="http://www.math.it/formulario/images/poliedri/rotondi/Image511.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="74" /></span></td><td align="center" class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><img alt="cono" height="187" src="http://www.math.it/formulario/images/poliedri/rotondi/cono.gif" width="179" /></span></td></tr>
298. <tr><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
299. <b><span style="color: #0b5394;">Tronco di cono</span></b></div>
300. <span style="color: #0b5394;">Consideriamo un cono e tagliamolo con un piano parallelo al piano della base: otteniamo due figure, una è ancora un cono, l’altra è un <b>tronco di cono</b>.</span><br />
301. <span style="color: #0b5394;">Il <b>tronco di cono</b> è un solido attenuto dalla rotazione di un trapezio rettangolo attorno al lato perpendicolare alle basi.</span><br />
302. <span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Proprietà</span>. La superficie laterale di un tronco di cono è equivalente a un trapezio avente per basi le due circonferenze di base del tronco e per altezza il suo apotema.</span><br />
303. <span style="color: #0b5394;">L’area della <b>superficie laterale</b> di un tronco di cono si ottiene moltiplicando la somma delle misure delle lunghezze delle due circonferenze di base per la misura dell’apotema e dividendo tale prodotto per due:<br /><img alt="formula" class="img-middle" height="26" src="http://www.math.it/formulario/images/poliedri/rotondi/Image512.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="109" />, dove l’apotema è la lunghezza del lato obliquo del tronco di cono: <img alt="apotema" class="img-middle" height="34" src="http://www.math.it/formulario/images/poliedri/rotondi/apotema.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="128" /></span><br />
304. <span style="color: #0b5394;">L’area della <b>superficie totale</b> di un tronco di cono si ottiene sommando la superficie laterale e l’area delle due basi:<br /><img alt="formula" class="img-middle" height="24" src="http://www.math.it/formulario/images/poliedri/rotondi/Image513.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="113" />. In modo equivalente si può scrivere in funzione dei raggi: <img alt="formula" class="img-middle" height="32" src="http://www.math.it/formulario/images/poliedri/rotondi/Image526.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="193" />.</span><br />
305. <span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Proprietà</span>. Per il principio di Cavalieri, un tronco di cono e un tronco di piramide aventi basi equivalenti e altezze congruenti sono equivalenti.</span><br />
306. <span style="color: #0b5394;">Il <b>volume</b>di un tronco di cono si ottiene moltiplicando la misura dell’altezza per la somma delle aree delle due basi con la radice quadrata del loro prodotto, e dividendo tale prodotto per tre:<br /><img alt="formula" class="img-middle" height="52" src="http://www.math.it/formulario/images/poliedri/rotondi/Image514.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="188" />.<br />In modo equivalente il volume si può scrivere in funzione dei raggi: <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/poliedri/rotondi/Image525.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="164" /> .</span></td><td align="center" class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><img alt="tronco di cono" height="148" src="http://www.math.it/formulario/images/poliedri/rotondi/tronco-cono.gif" width="180" /></span></td></tr>
307. <tr><td style="font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
308. <b><span style="color: #0b5394;">Sfera e superficie sferica</span></b></div>
309. <span style="color: #0b5394;">La <b>sfera</b> è un solido ottenuto dalla rotazione completa di un semicerchio attorno al proprio diametro, il raggio e il centro del semicerchio sono il raggio e il centro della sfera.</span><br />
310. <span style="color: #0b5394;">La <b>superficie sferica </b>è l’insieme di tutti e solo i punti dello spazio che hanno la stessa distanza da un punto interno detto centro.</span><br />
311. <span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Proprietà</span>. La superficie sferica è equivalente alla superficie laterale del cilindro equilatero circoscritto ad essa.</span><span style="color: #0b5394;">L’area della <b>superficie sferica</b> si ottiene moltiplicando per quattro l’area del suo cerchio massimo:<br /><img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/poliedri/rotondi/Image515.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="61" /></span><br />
312. <span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Proprietà</span>. Una sfera è equivalente a un cono avente per altezza il raggio della sfera e per raggio di base il diametro della sfera.</span><br />
313. <span style="color: #0b5394;">Il <b>volume</b> della sfera si ottiene moltiplicando <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/poliedri/rotondi/Image516.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="28" />per il cubo del suo raggio:<br /><img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/poliedri/rotondi/Image517.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="66" /></span></td><td align="center" style="font-size: 0.9em;"><span style="color: #0b5394;"><img alt="sfera" height="164" src="http://www.math.it/formulario/images/poliedri/rotondi/sfera.gif" width="167" /></span></td></tr>
314. </tbody></table>
315. </div>
316. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/545663170230027516/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-solida-solidi-di-rotazione.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/545663170230027516'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/545663170230027516'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-solida-solidi-di-rotazione.html' title='Geometria Solida. Solidi di rotazione. Cilindro, cono, tronco di cono, sfera'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-1475683196771883761</id><published>2016-03-13T16:36:00.003-07:00</published><updated>2016-03-13T16:39:27.455-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Geometria dello spazio"/><category scheme="http://www.blogger.com/atom/ns#" term="Geometria Solida. Poliedri. Piramide e tronco di piramide"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>Geometria Solida. Poliedri. Piramide e tronco di piramide  </title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
317. <span style="color: #0b5394;"><br /></span>
318. <table border="0" cellpadding="1" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
319. <tr><th style="background-color: #660066; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;" valign="top" width="27%"><div align="center">
320. <b><span style="color: #0b5394;">superficie laterale</span></b></div>
321. </th><th style="background-color: #660066; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;" valign="top" width="22%"><div align="center">
322. <b><span style="color: #0b5394;">superficie totale</span></b></div>
323. </th><th style="background-color: #660066; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;" valign="top" width="31%"><div align="center">
324. <b><span style="color: #0b5394;">volume</span></b></div>
325. </th></tr>
326. <tr valign="middle"><td align="left" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="middle" width="20%"><b><span style="color: #0b5394;">piramide qualsiasi</span></b></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="27%"><span style="color: #0b5394;"> </span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="22%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/piramidi/Image398.gif" width="77" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="31%"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poliedri/piramidi/Image399.gif" width="66" /></span></td></tr>
327. <tr valign="middle"><td align="left" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="middle" width="20%"><b><span style="color: #0b5394;">piramide retta</span></b></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="27%"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poliedri/piramidi/Image400.gif" width="72" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="22%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/piramidi/Image398.gif" width="77" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="31%"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poliedri/piramidi/Image399.gif" width="66" /></span></td></tr>
328. <tr valign="middle"><td align="left" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="middle" width="20%"><b><span style="color: #0b5394;">tronco di piramide</span></b></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="27%"><span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poliedri/piramidi/Image401.gif" width="121" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="22%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/piramidi/Image402.gif" width="111" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="31%"><span style="color: #0b5394;"><img alt="formula" height="51" src="http://www.math.it/formulario/images/poliedri/piramidi/Image403.gif" width="189" /></span></td></tr>
329. </tbody></table>
330. <span style="color: #0b5394;"><br style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 23.04px;" /></span>
331. <table border="0" cellpadding="1" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
332. <tr><td class="dividisopra" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
333. <b><span style="color: #0b5394;">Piramide</span></b></div>
334. <span style="color: #0b5394;">La <b>piramide</b> è un <a href="http://www.math.it/formulario/poliedri.htm" style="text-decoration: none;">poliedro</a> limitato da un poligono qualsiasi e da tanti triangoli quanti sono i lati di questo poligono, aventi tutti un vertice in comune.</span></td><td class="dividisopra" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;" valign="top"><span style="color: #0b5394;"> </span></td></tr>
335. <tr><td align="center" style="font-size: 0.9em;"><span style="color: #0b5394;"><img alt="piramide" height="259" src="http://www.math.it/formulario/images/poliedri/piramidi/piramide.gif" width="248" /></span></td><td style="font-size: 0.9em;" valign="top"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
336. <b><span style="color: #0b5394;">LEGENDA</span></b></div>
337. <span style="color: #0b5394;">V vertice<br />ABCDEF base (poligono di base)<br />VAB faccia laterale (triangolo)<br />VH altezza (distanza tra il vertice e la base)<br />VM apotema<br />H piede dell’altezza<br />VB spigolo laterale<br />AB spigolo di base</span></td></tr>
338. <tr><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Una <b>piramide</b> si dice <b>retta</b> se il poligono di base è circoscrittibile a una circonferenza e il piede dell’altezza coincide con il centro di questa circonferenza.</span><br />
339. <span style="color: #0b5394;">L’<b>apotema di una piramide retta</b> è l’altezza di una delle sue facce.</span><br />
340. <span style="color: #0b5394;">Una <b>piramide</b> si dice <b>regolare</b> se è retta ed il poligono di base è un poligono regolare.</span></td><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><img alt="apotema di una piramide retta" height="150" src="http://www.math.it/formulario/images/poliedri/piramidi/apotema_piramide.gif" width="149" /></span></td></tr>
341. <tr><td style="font-size: 0.9em;" valign="top"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
342. <b><span style="color: #0b5394;">Tronco di piramide</span></b></div>
343. <span style="color: #0b5394;">Tagliando una piramide con un piano parallelo alla base si ottengono due solidi: uno è ancora una piramide , l’altro è un <b>tronco di piramide</b>. I due poligoni che lo delimitano costituiscono le <b>basi</b> del tronco di piramide, e le <b>facce laterali</b> sono dei trapezi. La distanza tra le basi è l’<b>altezza</b> del solido.</span><br />
344. <span style="color: #0b5394;">Un <b>tronco di piramide</b> si dice <b>retto</b> se è stato ottenuto da una piramide retta.</span><br />
345. <span style="color: #0b5394;">Un <b>tronco di piramide</b> si dice <b>regolare</b> se è stato ottenuto da una piramide regolare.<br />Le facce laterali di un tronco di piramide regolare sono tutti trapezi isosceli congruenti.<br />L’altezza di uno qualsiasi di questi trapezi è l’<b>apotema</b> del tronco di piramide.</span></td><td style="font-size: 0.9em;"><span style="color: #0b5394;"><img alt="tronco di piramide" height="126" src="http://www.math.it/formulario/images/poliedri/piramidi/troncopiramide.gif" width="253" /></span></td></tr>
346. </tbody></table>
347. </div>
348. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/1475683196771883761/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-solida-poliedri-piramide-e.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/1475683196771883761'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/1475683196771883761'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-solida-poliedri-piramide-e.html' title='Geometria Solida. Poliedri. Piramide e tronco di piramide  '/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-8051940975709581209</id><published>2016-03-13T16:35:00.002-07:00</published><updated>2016-03-13T16:39:27.472-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="cubo"/><category scheme="http://www.blogger.com/atom/ns#" term="Geometria dello spazio"/><category scheme="http://www.blogger.com/atom/ns#" term="Geometria Solida. Poliedri. Prisma"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><category scheme="http://www.blogger.com/atom/ns#" term="parallelpipedo"/><title type='text'>Geometria Solida. Poliedri. Prisma, parallelpipedo, cubo</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
349. <span style="color: #0b5394;"><br /></span>
350. <table border="0" cellpadding="1" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
351. <tr><th nowrap="nowrap" style="background-color: #660066; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;" width="22%"><div align="center">
352. <b><span style="color: #0b5394;">diagonale</span></b></div>
353. </th><th nowrap="nowrap" style="background-color: #660066; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;" width="19%"><div align="center">
354. <b><span style="color: #0b5394;">superficie laterale</span></b></div>
355. </th><th nowrap="nowrap" style="background-color: #660066; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;" width="19%"><div align="center">
356. <b><span style="color: #0b5394;">superficie totale</span></b></div>
357. </th><th nowrap="nowrap" style="background-color: #660066; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;" width="13%"><div align="center">
358. <b><span style="color: #0b5394;">volume</span></b></div>
359. </th></tr>
360. <tr><td align="left" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="27%"><b><span style="color: #0b5394;">prisma retto</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="22%"><span style="color: #0b5394;"> </span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="19%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/prismi/Image404.gif" width="72" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="19%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/prismi/Image405.gif" width="90" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="13%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/prismi/Image406.gif" width="66" /></span></td></tr>
361. <tr><td align="left" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="27%"><b><span style="color: #0b5394;">parallelepipedo retto</span></b></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="22%"><span style="color: #0b5394;"> </span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="19%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/prismi/Image404.gif" width="72" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="19%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/prismi/Image405.gif" width="90" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="13%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/prismi/Image406.gif" width="66" /></span></td></tr>
362. <tr><td align="left" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="27%"><b><span style="color: #0b5394;">parallelepipedo rettangolo</span></b></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="22%"><span style="color: #0b5394;"><img alt="formula" height="26" src="http://www.math.it/formulario/images/poliedri/prismi/Image407.gif" width="122" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="19%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/prismi/Image404.gif" width="72" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="19%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/prismi/Image405.gif" width="90" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="13%"><span style="color: #0b5394;"><img alt="formula" height="18" src="http://www.math.it/formulario/images/poliedri/prismi/Image408.gif" width="73" /></span></td></tr>
363. <tr><td align="left" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="27%"><b><span style="color: #0b5394;">cubo</span></b></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="22%"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/prismi/Image409.gif" width="55" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="19%"><span style="color: #0b5394;"><img alt="formula" height="25" src="http://www.math.it/formulario/images/poliedri/prismi/Image410.gif" width="55" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="19%"><span style="color: #0b5394;"><img alt="formula" height="25" src="http://www.math.it/formulario/images/poliedri/prismi/Image411.gif" width="55" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" width="13%"><span style="color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/poliedri/prismi/Image412.gif" width="42" /></span></td></tr>
364. </tbody></table>
365. <span style="color: #0b5394;"><br style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 23.04px;" /></span>
366. <table border="0" cellpadding="1" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
367. <tr><td class="dividisoprasotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
368. <b><span style="color: #0b5394;">Prismi</span></b></div>
369. <span style="color: #0b5394;">Il <b>prisma</b> è un <a href="http://www.math.it/formulario/poliedri.htm" style="text-decoration: none;">poliedro</a> limitato da due poligoni uguali e paralleli (basi) e da tanti parallelogrammi (facce laterali) quanti sono i lati del poligono di base.</span><br />
370. <blockquote>
371. <span style="color: #0b5394;"><b>prisma obliquo</b>: se tutte le facce laterali sono parallelogrammi e l’altezza non coincide con uno degli spigoli</span><br />
372. <span style="color: #0b5394;"><b>prisma retto</b>: se tutte le facce laterali sono perpendicolari alle basi e l’altezza coincide con uno degli spigoli</span><br />
373. <span style="color: #0b5394;"><b>prisma regolare</b>: se è retto e le basi sono poligoni regolari (le facce laterali sono rettangoli uguali fra loro).</span></blockquote>
374. </td><td align="center" class="dividisoprasotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><img alt="figura di un prisma" height="162" src="http://www.math.it/formulario/images/poliedri/prismi/prisma.gif" width="125" /></span></td></tr>
375. <tr><td style="font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
376. <b><span style="color: #0b5394;">Prismi particolari</span></b></div>
377. <blockquote>
378. <span style="color: #0b5394;"><b>Parallelepipedo</b><br />Un <b>parallelepipedo</b> è un prisma le cui basi sono dei parallelogrammi.<br />Un parallelepipedo può essere:</span><br />
379. <blockquote>
380. <span style="color: #0b5394;"><b>retto</b>: se tutte le sue facce sono perpendicolari alle basi (le facce sono dei rettangoli e le basi dei parallelogrammi)</span><br />
381. <span style="color: #0b5394;"><b>rettangolo</b>: se è retto e le sue basi sono dei rettangoli (tutte e sei le facce sono rettangoli uguali e paralleli a due a due)</span></blockquote>
382. </blockquote>
383. <blockquote>
384. <span style="color: #0b5394;"><b>Cubo</b><br />Il <b>cubo</b> è un parallelepipedo rettangolo con le tre dimensioni uguali tra loro.<br />Il cubo è un <a href="http://www.math.it/formulario/poliedri_regolari.htm" style="text-decoration: none;">poliedro regolare</a> limitato da sei facce quadrate (esaedro).</span></blockquote>
385. </td><td align="center" style="font-size: 0.9em;"><span style="color: #0b5394;"><img alt="figura di un parallelpipedo" height="162" src="http://www.math.it/formulario/images/poliedri/prismi/parallelepipedo.gif" width="186" /></span></td></tr>
386. </tbody></table>
387. </div>
388. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/8051940975709581209/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-solida-poliedri-prisma.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/8051940975709581209'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/8051940975709581209'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-solida-poliedri-prisma.html' title='Geometria Solida. Poliedri. Prisma, parallelpipedo, cubo'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-6819676244398833582</id><published>2016-03-13T16:34:00.003-07:00</published><updated>2016-03-13T16:39:27.468-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Geometria dello spazio"/><category scheme="http://www.blogger.com/atom/ns#" term="Geometria Solida. Poliedri regolari"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>Geometria Solida. Poliedri regolari</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
389. <div style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 23.04px;">
390. <span style="color: #0b5394;">Un <b><a href="http://www.math.it/formulario/poliedri.htm" style="text-decoration: none;">poliedro</a></b> si dice <b>regolare</b> se tutte le sue facce sono poligoni regolari uguali fra loro e tutti i diedri e gli angoloidi sono uguali fra loro.<br />I poliedri regolari che si possono costruire sono 5, noti anche come <i>solidi platonici</i>.</span></div>
391. <table border="0" cellpadding="1" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 1.2em; margin: 0px; padding: 5px;"><tbody>
392. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"></td><th class="cornice" style="background-color: #660066; border: 1px solid rgb(238, 238, 238); font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><b><span style="color: #0b5394;">poligono regolare</span></b></th><th class="cornice" style="background-color: #660066; border: 1px solid rgb(238, 238, 238); font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><b><span style="color: #0b5394;">N° facce</span></b></th><th class="cornice" style="background-color: #660066; border: 1px solid rgb(238, 238, 238); font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><b><span style="color: #0b5394;">N° vertici</span></b></th><th class="cornice" style="background-color: #660066; border: 1px solid rgb(238, 238, 238); font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><b><span style="color: #0b5394;">N° spigoli</span></b></th><th class="cornice" style="background-color: #660066; border: 1px solid rgb(238, 238, 238); font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><b><span style="color: #0b5394;">N° spigoli concorrenti in un vertice</span></b></th><th class="cornice" style="background-color: #660066; border: 1px solid rgb(238, 238, 238); font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><b><span style="color: #0b5394;">altezza</span></b></th><th class="cornice" style="background-color: #660066; border: 1px solid rgb(238, 238, 238); font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><b><span style="color: #0b5394;">diagonale</span></b></th><th class="cornice" style="background-color: #660066; border: 1px solid rgb(238, 238, 238); font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><b><span style="color: #0b5394;">Area della superficie</span></b></th><th class="cornice" style="background-color: #660066; border: 1px solid rgb(238, 238, 238); font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><b><span style="color: #0b5394;">Volume</span></b></th></tr>
393. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Tetraedro</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">triangolo</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">4</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">4</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">6</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">3</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image012.gif" width="68" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image014.gif" width="64" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image016.gif" width="84" /></span></td></tr>
394. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Cubo o Esaedro</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">quadrato</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">6</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">8</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">12</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">3</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image018.gif" width="57" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image020.gif" width="50" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image022.gif" width="44" /></span></td></tr>
395. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Ottaedro</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">triangolo</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">8</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">6</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">12</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">4</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image024.gif" width="72" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image026.gif" width="77" /></span></td></tr>
396. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Dodecaedro</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">pentagono</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">12</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">20</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">30</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">3</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="49" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image028.gif" width="122" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="45" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image030.gif" width="105" /></span></td></tr>
397. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Icosaedro</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">triangolo</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">20</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">12</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">30</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">5</span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image032.gif" width="72" /></span></td><td align="center" class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="52" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image034.gif" width="112" /></span></td></tr>
398. </tbody></table>
399. <blockquote style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 23.04px;">
400. <span style="color: #0b5394;"><b class="evidenziato" style="background-color: #eeeeee; letter-spacing: 0.1em;">LEGENDA</b><br /><span style="border-color: initial; border-image-outset: initial; border-image-repeat: initial; border-image-slice: initial; border-image-source: initial; border-image-width: initial; border-width: initial;"><img alt="h" class="img-middle" height="18" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image002.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="13" /></span> = altezza<br /><span style="border-color: initial; border-image-outset: initial; border-image-repeat: initial; border-image-slice: initial; border-image-source: initial; border-image-width: initial; border-width: initial;"><img alt="s" class="img-middle" height="14" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image004.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="12" /></span> = spigolo<br /><span style="border-color: initial; border-image-outset: initial; border-image-repeat: initial; border-image-slice: initial; border-image-source: initial; border-image-width: initial; border-width: initial;"><img alt="d" class="img-middle" height="18" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image006.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="14" /></span>= diagonale<br /><span style="border-color: initial; border-image-outset: initial; border-image-repeat: initial; border-image-slice: initial; border-image-source: initial; border-image-width: initial; border-width: initial;"><img alt="S" class="img-middle" height="18" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image008.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="14" /></span> = Area della superficie totale<br /><span style="border-color: initial; border-image-outset: initial; border-image-repeat: initial; border-image-slice: initial; border-image-source: initial; border-image-width: initial; border-width: initial;"><img alt="V" class="img-middle" height="18" src="http://www.math.it/formulario/images/poliedri/poliedri_regolari/image010.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="16" /></span> = Volume</span></blockquote>
401. </div>
402. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/6819676244398833582/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-solida-poliedri-regolari.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/6819676244398833582'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/6819676244398833582'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-solida-poliedri-regolari.html' title='Geometria Solida. Poliedri regolari'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-8857482364481369263</id><published>2016-03-13T16:33:00.003-07:00</published><updated>2016-03-13T16:39:27.475-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Geometria dello spazio"/><category scheme="http://www.blogger.com/atom/ns#" term="Geometria Solida. Poliedri"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>Geometria Solida. Poliedri</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
403. <div style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 23.04px;">
404. <span style="color: #0b5394;">Le figure geometriche solide possono essere suddivise in due gruppi:<br />quelli la cui superficie è formata da soli poligoni detti <b>poliedri</b>, e quelli la cui superficie è curva detti<b>solidi rotondi</b>.</span></div>
405. <div style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 23.04px;">
406. <span style="color: #0b5394;">Un <b>poliedro</b> è un solido limitato da più poligoni posti su piani diversi e tali che ogni lato è comune a due soli di essi.</span></div>
407. <blockquote style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 23.04px;">
408. <span style="color: #0b5394;"><img alt="figura di un poliedro" height="162" src="http://www.math.it/formulario/images/poliedri/poliedro.gif" width="339" /></span></blockquote>
409. <div style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 23.04px;">
410. <span style="color: #0b5394;">Tra le facce gli spigoli e i vertici di un poliedro sussiste la<b> relazione di Eulero</b>: f + v = s + 2</span></div>
411. <div style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 23.04px;">
412. <span style="color: #0b5394;">I poliedri possono essere suddivisi in <b><a class="B" href="http://www.math.it/formulario/poliedri_regolari.htm" style="text-decoration: none;">poliedri regolari</a></b>, <b><a class="B" href="http://www.math.it/formulario/prismi.htm" style="text-decoration: none;">prismi</a></b> e <b><a class="B" href="http://www.math.it/formulario/piramidi.htm" style="text-decoration: none;">piramidi</a></b>, come è raffigurato nello schema.</span></div>
413. <blockquote style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 17.28px; line-height: 23.04px;">
414. <span style="color: #0b5394;"><img alt="figura: classificazione dei poliedri" height="175" src="http://www.math.it/formulario/images/poliedri/classsificazione-poliedri.gif" width="400" /> </span></blockquote>
415. </div>
416. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/8857482364481369263/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-solida-poliedri.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/8857482364481369263'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/8857482364481369263'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-solida-poliedri.html' title='Geometria Solida. Poliedri'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-1392464513366427204</id><published>2016-03-13T16:30:00.003-07:00</published><updated>2016-03-13T16:39:20.141-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Geometria del piano"/><category scheme="http://www.blogger.com/atom/ns#" term="Geometria dello spazio"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>Poligoni regolari e numeri fissi  </title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
417. <table border="0" cellpadding="3" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
418. <tr valign="top"><td class="divididestra" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;" width="63%"><span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Definizione</span>: si dice <b>regolare</b> un <b>poligono</b> equilatero ed equiangolo.</span></td><td align="right" class="more" style="background-image: url("../images/back_math-g.gif"); color: #777777; font-size: 0.9em; letter-spacing: 0.1em; line-height: 1.2em;" width="37%"><span style="color: #0b5394;"><b>Vedi anche</b>: <a href="http://www.math.it/formulario/poligoni_convessi.htm" style="text-decoration: none;">poligoni convessi</a> e<a href="http://www.math.it/formulario/poligoni_regolari.htm" style="text-decoration: none;">poligoni regolari</a></span></td></tr>
419. <tr valign="top"><td class="divididestra" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Proprietà</span>: ogni poligono regolare è inscrittibile e circoscrittibile, e le due circonferenze hanno lo stesso centro.</span><br />
420. <span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Definizione</span>: si dice <b>apotema</b> di un poligono regolare il raggio del cerchio inscritto nel poligono.</span><br />
421. <span style="color: #0b5394;">Se è noto il raggio <i>R</i> del cerchio circoscritto e il lato del poligono regolare, l’apotema si trova applicando il teorema di Pitagora.</span><br />
422. <span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Proprietà</span>: in ogni poligono regolare il rapporto tra l'apotema e il lato è costante, dipende solo dal numero dei lati del poligono. A tale costante del poligono si dà il nome di <i><b>numero fisso</b></i>: <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image415.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="42" /><br />Per trovare l'apotema, noto solo il lato del poligono regolare, si usa fornire nella geometria studiata nelle medie inferiori una tabella di <i>numeri fissi</i>.<br />L'apotema si trova moltiplicando il lato per la costante del poligono: <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image416.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="60" /></span></td><td align="center" style="font-size: 0.9em;" valign="top"><table border="0" cellpadding="3" cellspacing="0" style="line-height: 1.2em; margin: 0px; padding: 5px;"><tbody>
423. <tr><th style="background-color: #660066; color: white; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;" valign="top"><b><span style="color: #0b5394;">Poligono regolare</span></b></th><th style="background-color: #660066; color: white; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;" valign="top"><div align="center">
424. <i><span style="color: #0b5394;">f</span></i></div>
425. </th></tr>
426. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Triangolo</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">0,289</span></td></tr>
427. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Quadrato</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">0,5</span></td></tr>
428. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Pentagono</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">0,688</span></td></tr>
429. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Esagono</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">0,866</span></td></tr>
430. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Ettagono</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">1,038</span></td></tr>
431. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Ottagono</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">1,207</span></td></tr>
432. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Ennagono</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">1,374</span></td></tr>
433. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Decagono</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">1,539</span></td></tr>
434. </tbody></table>
435. </td></tr>
436. <tr valign="top"><td class="divididestra" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;">L'apotema si può calcolare con l'aiuto della trigonometria, nota l'ampiezza <i>α</i> dell’angolo del poligono: <img alt="formula" class="img-middle" height="44" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image418.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="72" />.<br />Poiché in ogni poligono regolare il rapporto tra l'area e il quadrato del suo lato è costante, dipende solo dal numero dei lati del poligono, indichiamo tale costante con <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image419.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="45" />.<br />L'<b>area del poligono regolare</b> si calcola : <img alt="formula" class="img-middle" height="24" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image420.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="68" /></span><br />
437. <span style="color: #0b5394;">Nella geometria studiata nelle medie inferiori si usa fornire una tabella di <i>costanti</i>.</span></td><td align="center" style="font-size: 0.9em;"><table border="0" cellpadding="3" cellspacing="0" style="line-height: 1.2em; margin: 0px; padding: 5px;"><tbody>
438. <tr valign="middle"><th style="background-color: #660066; color: white; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><b><span style="color: #0b5394;">Poligono regolare</span></b></th><th style="background-color: #660066; color: white; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><div align="center">
439. <i><span style="color: #0b5394;">φ</span></i></div>
440. </th></tr>
441. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Triangolo</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">0,433</span></td></tr>
442. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Quadrato</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">1</span></td></tr>
443. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Pentagono</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">1,720</span></td></tr>
444. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Esagono</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">2,598</span></td></tr>
445. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Ettagono</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">3,634</span></td></tr>
446. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Ottagono</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">4,828</span></td></tr>
447. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Ennagono</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">6,182</span></td></tr>
448. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">Decagono</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;" valign="top"><span style="color: #0b5394;">7,694</span></td></tr>
449. </tbody></table>
450. </td></tr>
451. </tbody></table>
452. </div>
453. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/1392464513366427204/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/poligoni-regolari-e-numeri-fissi.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/1392464513366427204'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/1392464513366427204'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/poligoni-regolari-e-numeri-fissi.html' title='Poligoni regolari e numeri fissi  '/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-5953482573167928955</id><published>2016-03-13T16:29:00.004-07:00</published><updated>2016-03-13T16:31:31.515-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Geometria del piano"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>Poligoni regolari</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
454. <table border="0" cellpadding="3" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
455. <tr><td class="divididestra" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Definizione</span>: si dice <b>regolare</b> un<b>poligono</b> equilatero ed equiangolo.</span><br />
456. <span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Proprietà</span>: ogni poligono regolare è inscrittibile e circoscrittibile, e le due circonferenze hanno lo stesso centro.</span><br />
457. <span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Definizione</span>: si dice <b>apotema</b> di un poligono regolare il raggio del cerchio inscritto nel poligono.</span><br />
458. <span style="color: #0b5394;">In generale in un <b>poligono regolare</b> con <i>n</i>lati di lato <i>l</i> e apotema <i>a</i>:<br /><img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image422.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="56" /><br /><img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image423.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="54" />(semiperimetro per apotema)</span></td><td style="font-size: 0.9em;"><div class="more" style="background-image: url("../images/back_math-g.gif"); color: #777777; letter-spacing: 0.1em; line-height: 1.2em;">
459. <span style="color: #0b5394;"><b class="evidenziato" style="background-color: #eeeeee; letter-spacing: 0.1em;">Vedi anche</b>: <a href="http://www.math.it/formulario/poligoni_convessi.htm" style="text-decoration: none;">poligoni convessi</a> | <a href="http://www.math.it/formulario/poligoni_regolari_numerifissi.htm" style="text-decoration: none;">poligoni regolari coi numeri fissi</a> | <a href="http://www.math.it/cabri/index.htm" style="text-decoration: none;">costruzioni geometriche dei poligoni regolari con Cabri II</a></span></div>
460. <span style="color: #0b5394;"><b>LEGENDA</b><br />lato : <i>l</i><br />altezza : <i>h</i><br />diagonale : <i>d</i><br />perimetro : 2<i>p</i><br />semiperimetro : <i>p</i><br />apotema : <i>a</i><br />raggio della circonferenza circoscritta : <i>R</i><br />raggio della circonferenza inscritta : <i>r</i><br />Area : <i>A</i></span></td></tr>
461. <tr><td colspan="2" style="font-size: 0.9em;" valign="top"><table border="0" cellpadding="3" cellspacing="0" style="line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
462. <tr><th style="background-color: #660066; color: white; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><b><span style="color: #0b5394;">Poligono</span></b></th><th align="center" style="background-color: #660066; color: white; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><b><span style="color: #0b5394;">angolo</span></b></th><th align="center" style="background-color: #660066; color: white; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><b><span style="color: #0b5394;">lato</span></b></th><th align="center" style="background-color: #660066; color: white; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><b><span style="color: #0b5394;">apotema</span></b></th><th align="center" style="background-color: #660066; color: white; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><b><span style="color: #0b5394;">perimetro</span></b></th><th align="center" style="background-color: #660066; color: white; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><span style="color: #0b5394;"><b>Area</b>(noto <i>l</i>)</span></th><th align="center" style="background-color: #660066; color: white; font-size: 1em; letter-spacing: 0.2em; padding-bottom: 5px; padding-top: 5px;"><span style="color: #0b5394;"><b>Area </b>(noto<i>R</i>)</span></th></tr>
463. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Triangolo</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">60°</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="24" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image424.gif" width="55" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image425.gif" width="42" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image426.gif" width="51" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image427.gif" width="66" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image428.gif" width="79" /></span></td></tr>
464. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Quadrato</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">90°</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="22" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image429.gif" width="57" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image430.gif" width="65" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image431.gif" width="53" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image432.gif" width="42" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="19" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image433.gif" width="55" /></span></td></tr>
465. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Pentagono convesso</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">108°</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image434.gif" width="109" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image435.gif" width="96" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image436.gif" width="51" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image437.gif" width="123" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image438.gif" width="129" /></span></td></tr>
466. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Pentagono stellato</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image439.gif" width="109" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image440.gif" width="94" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image441.gif" width="138" /></span></td></tr>
467. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Esagono</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">120°</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="18" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image442.gif" width="37" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image443.gif" width="63" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="v" height="21" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image444.gif" width="53" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image445.gif" width="77" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image446.gif" width="79" /></span></td></tr>
468. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Ottagono convesso</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">135°</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="27" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image447.gif" width="90" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image448.gif" width="98" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image449.gif" width="51" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="31" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image450.gif" width="107" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="22" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image451.gif" width="77" /></span></td></tr>
469. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Ottagono stellato</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="27" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image452.gif" width="91" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image453.gif" width="98" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="31" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image454.gif" width="110" /></span></td></tr>
470. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Decagono convesso</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">144°</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image455.gif" width="91" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image456.gif" width="113" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image457.gif" width="58" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image458.gif" width="120" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image459.gif" width="129" /></span></td></tr>
471. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Decagono stellato</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image460.gif" width="91" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image461.gif" width="111" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image462.gif" width="138" /></span></td></tr>
472. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><b><span style="color: #0b5394;">Dodecagono convesso</span></b></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;">150°</span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image463.gif" width="106" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image464.gif" width="110" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image465.gif" width="58" /></span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"> </span></td><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image466.gif" width="54" /></span></td></tr>
473. </tbody></table>
474. </td></tr>
475. <tr><td class="evidenziato" colspan="2" style="background-color: #eeeeee; font-size: 0.9em; font-weight: bold; letter-spacing: 0.1em;"><b><span style="color: #0b5394;">Altre proprietà:</span></b></td></tr>
476. <tr><td style="font-size: 0.9em;"><span style="color: #0b5394;"><b>Triangolo equilatero </b>L'altezza del triangolo equilatero: <img alt="formula" class="img-middle" height="45" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image467.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="55" /></span></td><td style="font-size: 0.9em;"><span style="color: #0b5394;"><b>Quadrato </b>La diagonale del quadrato noto il lato: <img alt="formula" class="img-middle" height="22" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image468.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="55" /><br />Il lato del quadrato nota la diagonale:<br /><img alt="formula" class="img-middle" height="45" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image469.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="59" /> ; <img alt="formula" class="img-middle" height="22" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image470.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="49" /></span></td></tr>
477. <tr><td style="font-size: 0.9em;"><span style="color: #0b5394;"><b>Pentagono regolare convesso</b><br />Il lato del pentagono regolare corrisponde alla <a href="http://www.math.it/cabri/sezaurea.htm" style="text-decoration: none;">sezione aurea</a> della sua diagonale: <img alt="formula" class="img-middle" height="45" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image471.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="78" /><br />La diagonale del pentagono regolare in funzione del lato: <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image472.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="93" /></span></td><td style="font-size: 0.9em;"><span style="color: #0b5394;"><b>Esagono regolare convesso </b>L'esagono regolare è inscrittibile in una circonferenza il cui raggio è uguale al lato dell'esagono</span><br />
478. <span style="color: #0b5394;"><b>Decagono regolare convesso</b>Il lato del decagono regolare convesso è uguale alla sezione aurea del raggio della circonferenza circoscritta: <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/poligoni/poligoni_regolari/Image455.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="91" /></span></td></tr>
479. </tbody></table>
480. </div>
481. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/5953482573167928955/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/poligoni-regolari.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/5953482573167928955'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/5953482573167928955'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/poligoni-regolari.html' title='Poligoni regolari'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-2652715373547184048</id><published>2016-03-13T16:29:00.000-07:00</published><updated>2016-03-13T16:31:31.512-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Geometria del piano"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>Poligoni convessi</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
482. <table border="0" cellpadding="3" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
483. <tr valign="top"><td class="divididestra" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;" width="59%"><span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Definizione</span>: si chiama <b>poligono convesso</b> la parte di piano delimitata da una poligonale chiusa convessa e dalla poligonale stessa che ne costituisce il perimetro.</span><br />
484. <table align="center" border="0" cellpadding="1" cellspacing="1" class="cornice" style="border: 1px solid rgb(238, 238, 238); line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
485. <tr align="center"><td style="font-size: 0.9em;"><span class="nota" style="line-height: 1.3em;"><span style="color: #0b5394;">Poligono convesso</span></span></td><td style="font-size: 0.9em;"><span class="nota" style="line-height: 1.3em;"><span style="color: #0b5394;">Poligono concavo</span></span></td></tr>
486. <tr align="center"><td style="font-size: 0.9em;"><span style="color: #0b5394;"><img alt="Poligono convesso" height="192" src="http://www.math.it/formulario/images/poligoni/poligono_convesso.gif" width="192" /></span></td><td style="font-size: 0.9em;"><span style="color: #0b5394;"><img alt="Poligono concavo" height="192" src="http://www.math.it/formulario/images/poligoni/poligono_concavo.gif" width="192" /></span></td></tr>
487. </tbody></table>
488. </td><td style="font-size: 0.9em;" width="41%"><div class="more" style="background-image: url("../images/back_math-g.gif"); color: #777777; letter-spacing: 0.1em; line-height: 1.2em;">
489. <span style="color: #0b5394;"><b>Vedi anche</b>: <a href="http://www.math.it/formulario/poligoni_regolari.htm" style="text-decoration: none;">poligoni regolari</a> |<a href="http://www.math.it/formulario/poligoni_regolari_numerifissi.htm" style="text-decoration: none;">poligoni regolari con i numeri fissi</a></span></div>
490. <span style="color: #0b5394;"><b>LEGENDA</b><br />semiperimetro : <i>p</i><br />raggio della circonferenza inscritta : <i>r</i><br />Area : <i>A</i></span></td></tr>
491. <tr valign="top"><td class="divididestra" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Teorema</span>: in un poligono ogni lato è minore del semiperimetro</span><br />
492. <span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Teorema</span>: la <b>somma degli angoli intern</b>i di un poligono di<i>n</i> lati vale <img alt="formula" class="img-middle" height="26" src="http://www.math.it/formulario/images/poligoni/Image413.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="60" /></span><br />
493. <span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Teorema</span>: la <b>somma degli angoli esterni</b> di un poligono convesso è uguale ad un angolo giro (360°), qualunque sia il numero dei suoi lati</span><br />
494. <span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Teorema</span>: in un poligono qualsiasi di <i>n</i> lati, per ogni vertice passano (<i>n</i>-3) diagonali</span><br />
495. <span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Teorema</span>: un poligono si può inscrivere in una circonferenza se gli assi di tutti i suoi lati si incontrano in un unico punto (<b>circocentro</b>)</span><br />
496. <span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Teorema</span>: un poligono si può circoscrivere ad una circonferenza se le bisettrici di tutti i suoi angoli si incontrano in un unico punto (<b>incentro</b>)</span></td><td style="font-size: 0.9em;"><span style="color: #0b5394;"><b>Area di un poligono qualsiasi</b>: si scompone il poligono in poligoni di cui si sa calcolare l’area; si sommano le aree di tali poligoni.</span><br />
497. <span style="color: #0b5394;"><b>Area di un poligono circoscritto ad una circonferenza</b> di raggio <i>r</i> :</span><br />
498. <span style="color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/poligoni/Image414.gif" width="58" /></span></td></tr>
499. </tbody></table>
500. </div>
501. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/2652715373547184048/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/poligoni-convessi.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/2652715373547184048'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/2652715373547184048'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/poligoni-convessi.html' title='Poligoni convessi'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-1642924561177866411</id><published>2016-03-13T16:28:00.003-07:00</published><updated>2016-03-13T16:31:31.508-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Geometria del piano"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>Quadrilateri</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
502. <table border="0" cellpadding="3" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; height: 350px; line-height: 1.2em; margin: 0px; padding: 5px; width: 99%px;"><tbody>
503. <tr valign="top"><td style="font-size: 0.9em;" valign="middle"><table border="0" cellpadding="3" cellspacing="0" class="cornice" style="border: 1px solid rgb(238, 238, 238); line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
504. <tr align="center"><td style="font-size: 0.9em;"><span style="color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
505. <tr><td align="center" class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><span style="color: #0b5394;">Muovi a tuo piacere i vertici del quadrilatero.</span></td></tr>
506. </tbody></table>
507. </td><td style="font-size: 0.9em;"><b><span style="color: #0b5394;">LEGENDA</span></b><br />
508. <span style="color: #0b5394;">AB = <i>c</i>, BC = <i>b</i>, CD = <i>a, </i>DA = <i>d, </i>DMC = a,<br /><i>p</i> = semiperimetro</span></td></tr>
509. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><b>» </b> <b>Calcolo dell’area</b>:</span><span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/quadrilateri/Image261.gif" width="161" /> </span><br />
510. <span style="color: #0b5394;"><b>» </b><b>Condizione di inscrittibilità</b>:</span><br />
511. <span style="color: #0b5394;"><img alt="formula" height="22" src="http://www.math.it/formulario/images/quadrilateri/Image262.gif" width="94" /></span><br />
512. <span style="color: #0b5394;"><b><b>» </b>Condizione di circoscrittibilità</b>:</span><br />
513. <span style="color: #0b5394;"><img alt="formula" height="22" src="http://www.math.it/formulario/images/quadrilateri/Image263.gif" width="139" /></span></td></tr>
514. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><b><b>» </b>Formule relative al quadrilatero inscrittibile</b>:</span><br />
515. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="30" src="http://www.math.it/formulario/images/quadrilateri/Image264.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="264" /> (Formula di Brahmagupta)</span><br />
516. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="22" src="http://www.math.it/formulario/images/quadrilateri/Image265.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="193" /> (Teorema di Tolomeo)</span><br />
517. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="45" src="http://www.math.it/formulario/images/quadrilateri/Image266.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="168" /> (Teorema di Legendre)</span><br />
518. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="55" src="http://www.math.it/formulario/images/quadrilateri/Image267.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="457" /> Raggio della circonferenza circoscritta</span><br />
519. </td></tr>
520. <tr valign="top"><td class="dividisopra" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><b><b>» </b>Trapezio</b>:</span><br />
521. <span style="color: #0b5394;"><img alt="formula" height="22" src="http://www.math.it/formulario/images/quadrilateri/Image268.gif" width="63" /></span><br />
522. <span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/quadrilateri/Image269.gif" width="147" /></span><br />
523. <span style="color: #0b5394;"><b><b>» </b>Trapezio isoscele</b>:è un particolare trapezio in cui i lati obliqui sono uguali</span><br />
524. <span style="color: #0b5394;"><img alt="formula" height="25" src="http://www.math.it/formulario/images/quadrilateri/Image270.gif" width="158" /></span><br />
525. <blockquote>
526. <span style="color: #0b5394;"><b><b>» </b>Proprietà del trapezio isoscele</b>:<br />- Gli angoli alle basi sono uguali<br />- Le diagonali sono uguali<br />- Il lato obliquo di un trapezio isoscele circoscritto ad un semicerchio è uguale alla metà della base maggiore<br />- Il lato obliquo di un trapezio isoscele circoscritto ad una circonferenza è uguale alla semisomma delle basi del trapezio stesso.</span></blockquote>
527. <span style="color: #0b5394;"><b><b>» </b>Trapezio rettangolo</b>: è un particolare trapezio in cui un lato è perpendicolare alle basi</span><br />
528. <span style="color: #0b5394;"><img alt="formula" height="25" src="http://www.math.it/formulario/images/quadrilateri/Image271.gif" width="158" /></span></td><td class="dividisopra" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><table border="0" cellpadding="3" cellspacing="0" class="cornice" style="border: 1px solid rgb(238, 238, 238); line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
529. <tr align="center"><td style="font-size: 0.9em;"><span style="color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
530. <tr><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><span style="color: #0b5394;"><b>Quadrilatero particolare</b>. <b>Trapezio</b> (una coppia di lati sta su rette tra loro parallele).<br />Muovi qualsiasi vertice del quadrilatero per variare le dimensioni e la disposizione della figura..</span></td></tr>
531. </tbody></table>
532. <table border="0" cellpadding="3" cellspacing="0" class="cornice" style="border: 1px solid rgb(238, 238, 238); line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
533. <tr align="center"><td style="font-size: 0.9em;"><span style="color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
534. <tr><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><span style="color: #0b5394;"><b>Quadrilatero particolare.</b> <b>Trapezio isoscele</b> (i lati obliqui sono tra loro congruenti).<br />Muovi il punto B per ruotare a piacere il quadrilatero o il punto A per variare le dimensioni.</span></td></tr>
535. </tbody></table>
536. </td></tr>
537. <tr valign="top"><td class="dividisopra" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><b><b>» </b>Parallelogramma</b>: è un quadrilatero con i lati opposti paralleli</span><br />
538. <span style="color: #0b5394;"><img alt="formula" height="25" src="http://www.math.it/formulario/images/quadrilateri/Image272.gif" width="158" /><br /><img alt="formula" height="25" src="http://www.math.it/formulario/images/quadrilateri/Image273.gif" width="158" /><br /><img alt="formula" height="25" src="http://www.math.it/formulario/images/quadrilateri/Image274.gif" width="174" /></span><br />
539. <span style="color: #0b5394;"><img alt="formula" height="22" src="http://www.math.it/formulario/images/quadrilateri/Image275.gif" width="107" /></span><br />
540. <span style="color: #0b5394;"><img alt="formula" height="25" src="http://www.math.it/formulario/images/quadrilateri/Image276.gif" width="169" /></span><br />
541. <blockquote>
542. <span style="color: #0b5394;"><b><b>» </b>Proprietà del </b><b>parallelogramma</b>:<br />- Gli angoli opposti sono uguali e gli adiacenti sono supplementari<br />- Ogni diagonale scompone il parallelogramma in due triangoli uguali<br />- Le diagonali si tagliano scambievolmente per metà</span></blockquote>
543. </td><td class="dividisopra" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><table border="0" cellpadding="3" cellspacing="0" style="line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
544. <tr align="center"><td style="font-size: 0.9em;"><span style="color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
545. <tr><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><span style="color: #0b5394;"><b>Quadrilatero particolare.</b> <b>Trapezio particolare. Parallelogramma</b> (i lati opposti sono congruenti e stanno su rette tra loro parallele).</span></td></tr>
546. </tbody></table>
547. </td></tr>
548. <tr valign="top"><td class="dividisopra" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><b><b>» </b>Rombo</b>: è un parallelogramma particolare in cui i quattro lati sono uguali</span><br />
549. <span style="color: #0b5394;"><img alt="formula" height="22" src="http://www.math.it/formulario/images/quadrilateri/Image277.gif" width="142" /><br /><img alt="formula" height="22" src="http://www.math.it/formulario/images/quadrilateri/Image278.gif" width="67" /></span><br />
550. <span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/quadrilateri/Image283.gif" width="118" /></span><br />
551. <blockquote>
552. <span style="color: #0b5394;"><b><b>» </b>Proprietà del rombo</b>:<br />- Gli angoli opposti sono uguali e gli adiacenti sono supplementari<br />- Le diagonali si tagliano scambievolmente per metà e sono fra loro perpendicolari<br />- Le diagonali sono bisettrici degli angoli, i cui vertici sono gli estremi delle diagonali</span></blockquote>
553. </td><td class="dividisopra" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><table border="0" cellpadding="3" cellspacing="0" class="cornice" style="border: 1px solid rgb(238, 238, 238); line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
554. <tr align="center"><td style="font-size: 0.9em;"><span style="color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
555. <tr><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><span style="color: #0b5394;"><b>Quadrilatero particolare.</b> <b>Parallelogramma</b><b>particolare. Rombo</b> (i lati sono tra loro congruenti e le diagonali stanno su rette tra loro perpendicolari).</span></td></tr>
556. </tbody></table>
557. </td></tr>
558. <tr valign="top"><td class="dividisopra" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><b><b>» </b>Rettangolo</b>: è un parallelogramma particolare in cui i lati adiacenti sono tra loro perpendicolari</span><br />
559. <span style="color: #0b5394;"><img alt="formula" height="22" src="http://www.math.it/formulario/images/quadrilateri/Image279.gif" width="65" /><br /><img alt="formula" height="22" src="http://www.math.it/formulario/images/quadrilateri/Image280.gif" width="105" /></span><br />
560. <span style="color: #0b5394;"><b><b>» </b>Quadrato</b>: è un rombo particolare in cui i lati adiacenti sono tra loro perpendicolari</span><br />
561. <span style="color: #0b5394;"><img alt="formula" height="25" src="http://www.math.it/formulario/images/quadrilateri/Image281.gif" width="162" /><br /><img alt="formula" height="25" src="http://www.math.it/formulario/images/quadrilateri/Image282.gif" width="82" /></span></td><td class="dividisopra" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><table border="0" cellpadding="3" cellspacing="0" class="cornice" style="border: 1px solid rgb(238, 238, 238); line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
562. <tr align="center"><td style="font-size: 0.9em;"><span style="color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
563. <tr><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><span style="color: #0b5394;"><b>Quadrilatero particolare.</b> <b>Rombo </b><b>particolare. Quadrato </b>(è un rombo in cui i lati adiacenti sono tra loro perpendicolari).</span></td></tr>
564. </tbody></table>
565. </td></tr>
566. </tbody></table>
567. </div>
568. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/1642924561177866411/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/quadrilateri.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/1642924561177866411'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/1642924561177866411'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/quadrilateri.html' title='Quadrilateri'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-8910932593913220953</id><published>2016-03-13T16:27:00.002-07:00</published><updated>2016-03-13T16:31:31.527-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Geometria del piano"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>Cerchio e circonferenza</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
569. <table align="center" border="0" cellpadding="3" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; height: 350px; line-height: 1.2em; margin: 0px; padding: 5px; width: 99%px;"><tbody>
570. <tr valign="top"><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" width="50%"><span style="color: #0b5394;">Lunghezza della circonferenza: <img alt="formula" class="img-middle" src="http://www.math.it/formulario/images/cerchio/cerchi1.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" v:shapes="_x0000_i1025" /></span><br />
571. <span style="color: #0b5394;">Area del cerchio: <img alt="formula" class="img-middle" src="http://www.math.it/formulario/images/cerchio/cerchi2.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" v:shapes="_x0000_i1026" /></span><br />
572. <span style="color: #0b5394;">Lunghezza dell'arco: <img alt="formula" class="img-middle" src="http://www.math.it/formulario/images/cerchio/cerchi3.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" v:shapes="_x0000_i1027" /></span><br />
573. <span style="color: #0b5394;">Area del settore circolare: <img alt="formula" class="img-middle" src="http://www.math.it/formulario/images/cerchio/cerchi4.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" v:shapes="_x0000_i1028" />; <img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/cerchio/cerchi4b.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" v:shapes="_x0000_i1028" width="69" /></span><br />
574. <span style="color: #0b5394;">Area del semicerchio: <img alt="formula" class="img-middle" src="http://www.math.it/formulario/images/cerchio/cerchi5.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" v:shapes="_x0000_i1029" /></span><br />
575. <span style="color: #0b5394;">Area del quadrante: <img alt="formula" class="img-middle" src="http://www.math.it/formulario/images/cerchio/cerchi6.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" v:shapes="_x0000_i1030" /></span><br />
576. <span style="color: #0b5394;">Area della corona circolare: <img alt="formula" class="img-middle" src="http://www.math.it/formulario/images/cerchio/cerchi7.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" v:shapes="_x0000_i1031" /></span><br />
577. <span style="color: #0b5394;">Area del segmento circolare: si trova come differenza fra l'area di un settore e l'area di un triangolo.</span></td><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" width="50%"><blockquote>
578. <b><span style="color: #0b5394;">LEGENDA</span></b><br />
579. <span style="color: #0b5394;">Raggio = <i>r</i></span></blockquote>
580. <table border="0" cellpadding="3" cellspacing="0" style="line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
581. <tr><td style="font-size: 0.9em;"><span style="color: #0b5394;"><img alt="semicerchio" height="169" src="http://www.math.it/formulario/images/cerchio/semicerchio.gif" width="190" /></span></td><td style="font-size: 0.9em;"><span style="color: #0b5394;"><img alt="settore" height="173" src="http://www.math.it/formulario/images/cerchio/settore.gif" width="174" /></span></td></tr>
582. <tr><td style="font-size: 0.9em;"><span style="color: #0b5394;"><img alt="corona circolare" height="173" src="http://www.math.it/formulario/images/cerchio/corona.gif" width="173" /></span></td><td style="font-size: 0.9em;"><span style="color: #0b5394;"><img alt="segmento circolare - segmento a due basi - quadrante" height="172" src="http://www.math.it/formulario/images/cerchio/quadrante.gif" width="171" /></span></td></tr>
583. </tbody></table>
584. </td></tr>
585. <tr valign="top"><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><b>» </b><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Teorema della corda:</span> (vedi anche il<a href="http://www.math.it/formulario/triangolo.htm" style="text-decoration: none;">terorema dei seni</a>)</span><br />
586. <span style="color: #0b5394;"><img alt="formula" class="img-middle" src="http://www.math.it/formulario/images/cerchio/cerchi8.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" />   </span><br />
587. <span style="color: #0b5394;"><img alt="formula" class="img-middle" src="http://www.math.it/formulario/images/cerchio/cerchi9.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" />  </span><br />
588. <span style="color: #0b5394;">dove <span class="greco" style="font-family: Courier, Times, Arial, Helvetica, sans-serif; font-size: 1.6em; font-style: italic; letter-spacing: 0.2em;">α</span> è uno qualsiasi degli angoli alla circonferenza inscritti nell'arco maggiore <i>AB .</i></span></td><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><table border="0" cellpadding="3" cellspacing="0" style="line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
589. <tr valign="top"><td style="font-size: 0.9em;"><span style="color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
590. <tr valign="top"><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><div class="nota" style="line-height: 1.3em;">
591. <span style="color: #0b5394;">Qui sopra puoi sperimentare il <b>Teorema della corda</b>, variando l'ampiezza dell'angolo <span class="greco" style="font-family: Courier, Times, Arial, Helvetica, sans-serif; font-size: 1.6em; font-style: italic; letter-spacing: 0.2em;">α</span></span></div>
592. </td></tr>
593. </tbody></table>
594. </td></tr>
595. <tr valign="top"><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><b>» </b><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Teorema delle corde</span>:</span><br />
596. <span style="color: #0b5394;"><img alt="formula" class="img-middle" src="http://www.math.it/formulario/images/cerchio/cerchi11.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" />  , ossia</span><br />
597. <span style="color: #0b5394;"><img alt="formula" class="img-middle" src="http://www.math.it/formulario/images/cerchio/cerchi12.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" /></span></td><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><table border="0" cellpadding="3" cellspacing="0" style="line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
598. <tr valign="top"><td style="font-size: 0.9em;"><span style="color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
599. <tr valign="top"><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><span style="color: #0b5394;">Qui sopra puoi verificare la validità del <b>Teorema delle corde</b>.</span></td></tr>
600. </tbody></table>
601. </td></tr>
602. <tr valign="top"><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><b>» </b><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Teorema delle secanti</span>:</span><br />
603. <span style="color: #0b5394;"><img alt="formula" class="img-middle" src="http://www.math.it/formulario/images/cerchio/cerchi13.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" />  , ossia</span><br />
604. <span style="color: #0b5394;"><img align="absmiddle" alt="formula" src="http://www.math.it/formulario/images/cerchio/cerchi14.gif" /></span></td><td rowspan="2" style="font-size: 0.9em;"><table border="0" cellpadding="3" cellspacing="0" style="line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
605. <tr valign="top"><td style="font-size: 0.9em;"><span style="color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
606. <tr valign="top"><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><span style="color: #0b5394;">Prova a muovere i punti A o B dei due segmenti o il punto P esterno alla circonferenza per vedere come varia la situazione geometrica descritta dal <b>teorema delle secanti</b>.</span><br />
607. <span style="color: #0b5394;">Se muovi un estremo del segmento lungo la circonferenza, per es. D, fino a farlo coincidere con l'altro, C, ottieni la situazione descritta nel <b>teorema della tangente e della secante</b>, dove C=D=T.</span></td></tr>
608. </tbody></table>
609. </td></tr>
610. <tr valign="top"><td style="font-size: 0.9em;"><span style="color: #0b5394;"><b>» </b><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">Teorema della tangente e della secante</span>:</span><br />
611. <span style="color: #0b5394;"><img alt="formula" class="img-middle" src="http://www.math.it/formulario/images/cerchio/cerchi15.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" /> , ossia</span><br />
612. <span style="color: #0b5394;"><img alt="formula" class="img-middle" src="http://www.math.it/formulario/images/cerchio/cerchi16.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" /></span></td></tr>
613. </tbody></table>
614. </div>
615. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/8910932593913220953/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/cerchio-e-circonferenza.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/8910932593913220953'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/8910932593913220953'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/cerchio-e-circonferenza.html' title='Cerchio e circonferenza'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-7040422529474058097</id><published>2016-03-13T16:26:00.002-07:00</published><updated>2016-03-13T16:31:31.519-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Geometria del piano"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>Triangoli rettangoli</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
616. <table border="0" cellpadding="3" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
617. <tr valign="top"><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" width="50%"><table border="0" cellpadding="3" cellspacing="0" class="cornice" style="border: 1px solid rgb(238, 238, 238); line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
618. <tr><td align="center" style="font-size: 0.9em;"><span style="background-color: white; color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
619. <tr><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><span style="background-color: white; color: #0b5394;">Prova a muovere i vertici del triangolo per vedere come variano i suoi elementi.</span></td></tr>
620. </tbody></table>
621. </td><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" width="50%"><b><span style="background-color: white; color: #0b5394;">LEGENDA</span></b><br />
622. <span style="background-color: white; color: #0b5394;">AB = <i>c (cateto)</i>, AC = <i>b</i> (cateto), BC = <i>a</i>(ipotenusa)<i><br /></i>BAC = a = 90°, ABC = b, ACB = g<br />AH = <i>h</i>, altezza<br />AM = <i>m</i>, mediana<br /><i>A </i>= area</span><br />
623. <br />
624. <span style="background-color: white; color: #0b5394;"><img alt="indicatore" class="img-middle" height="9" src="http://www.math.it/images/frecver.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="9" /><a href="http://www.math.it/formulario/triangolo.htm" style="text-decoration: none;">vedi anche triangoli qualsiasi</a></span></td></tr>
625. <tr valign="top"><td style="font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
626. <span style="background-color: white; color: #0b5394;"><b>» </b>Teorema di Pitagora:</span></div>
627. <span style="background-color: white; color: #0b5394;">In un triangolo rettangolo il quadrato costruito sull'ipotenusa è equivalente alla somma dei quadrati costruiti sui due cateti.</span><br />
628. <span style="background-color: white; color: #0b5394;"><img alt="formula del teorema di Pitagora" height="22" src="http://www.math.it/formulario/images/triangoloretto/Image658.gif" width="126" /></span></td><td rowspan="3" style="font-size: 0.9em;"><table border="0" cellpadding="3" cellspacing="0" class="cornice" style="border: 1px solid rgb(238, 238, 238); line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
629. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="background-color: white; color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
630. <tr valign="top"><td class="nota" height="1" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><span style="background-color: white; color: #0b5394;">Qui sopra puoi sperimentare sia il Teorema di Pitagora (<a href="http://www.math.it/cabri/pitagora.htm" style="text-decoration: none;">vedi costruzione</a>), sia il 1° Teorema di Euclide (<a href="http://www.math.it/cabri/euclide1.htm" style="text-decoration: none;">vedi costruzione</a>).<br />Qui sotto puoi verificare la validità del 2° Teorema di Euclide (<a href="http://www.math.it/cabri/euclide2.htm" style="text-decoration: none;">vedi costruzione</a>).</span></td></tr>
631. <tr><td class="cornice" style="border: 1px solid rgb(238, 238, 238); font-size: 0.9em;"><span style="background-color: white; color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
632. </tbody></table>
633. </td></tr>
634. <tr valign="top"><td style="font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
635. <span style="background-color: white; color: #0b5394;"><b>» </b>Primo teorema di Euclide:</span></div>
636. <span style="background-color: white; color: #0b5394;">In un triangolo rettangolo il quadrato costruito su un cateto è equivalente al rettangolo che ha per dimensioni la sua proiezione sull'ipotenusa e l'ipotenusa stessa.</span><br />
637. <span style="background-color: white; color: #0b5394;"><img alt="formula del primo teorema di euclide" height="22" src="http://www.math.it/formulario/images/triangoloretto/Image659.gif" width="106" /> ; <img alt="formula del primo teorema di euclide" height="22" src="http://www.math.it/formulario/images/triangoloretto/Image660.gif" width="107" /></span></td></tr>
638. <tr valign="top"><td style="font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
639. <span style="background-color: white; color: #0b5394;"><b>» </b>Secondo teorema di Euclide:</span></div>
640. <span style="background-color: white; color: #0b5394;">In un triangolo rettangolo l'altezza è media proporzionale tra le proiezioni dei due cateti sull'ipotenusa.</span><br />
641. <span style="background-color: white; color: #0b5394;"><img alt="formula del secondo teorema di euclide" height="22" src="http://www.math.it/formulario/images/triangoloretto/Image661.gif" width="111" /></span></td></tr>
642. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><span style="background-color: white; color: #0b5394;"><b>» </b><b>Proprietà della mediana</b>:</span><br />
643. <span style="background-color: white; color: #0b5394;"><img alt="formula" height="18" src="http://www.math.it/formulario/images/triangoloretto/Image662.gif" width="118" /></span></td></tr>
644. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><span style="background-color: white; color: #0b5394;"><b>» </b><b>Calcolo dell'area</b>:</span><br />
645. <span style="background-color: white; color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangoloretto/Image663.gif" width="58" />, <img alt="formula" height="41" src="http://www.math.it/formulario/images/triangoloretto/Image664.gif" width="61" /></span></td></tr>
646. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><span style="background-color: white; color: #0b5394;"><b>» </b><b>Misura dell'altezza noti i lati</b>:</span><br />
647. <span style="background-color: white; color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangoloretto/Image665.gif" width="55" /></span></td></tr>
648. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><span style="background-color: white; color: #0b5394;"><b>» </b><b>Relazione fra i lati e il raggio della circonferenza inscritta</b>:</span><br />
649. <span style="background-color: white; color: #0b5394;"><img alt="formula" height="18" src="http://www.math.it/formulario/images/triangoloretto/Image666.gif" width="91" /></span></td></tr>
650. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><span style="background-color: white; color: #0b5394;"><b>» </b><b>1° teorema sui triangoli rettangoli</b>:</span><br />
651. <span style="background-color: white; color: #0b5394;">In un triangolo rettangolo la misura di un cateto è uguale al prodotto dell'ipotenusa per il seno dell'angolo opposto o per il coseno dell'angolo adiacente</span><br />
652. <span style="background-color: white; color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/triangoloretto/Image667.gif" width="145" /> , <img alt="formula" height="21" src="http://www.math.it/formulario/images/triangoloretto/Image668.gif" width="146" /></span></td></tr>
653. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><span style="background-color: white; color: #0b5394;"><b>» </b><b>2° teorema sui triangoli rettangoli</b>:</span><br />
654. <span style="background-color: white; color: #0b5394;">In un triangolo rettangolo la misura di un cateto è uguale al prodotto dell'altro cateto per la tangente dell'angolo opposto o per la cotangente dell'angolo adiacente</span><br />
655. <span style="background-color: white; color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/triangoloretto/Image669.gif" width="130" /> , <img alt="formula" height="21" src="http://www.math.it/formulario/images/triangoloretto/Image670.gif" width="130" /></span></td></tr>
656. </tbody></table>
657. </div>
658. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/7040422529474058097/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/triangoli-rettangoli.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/7040422529474058097'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/7040422529474058097'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/triangoli-rettangoli.html' title='Triangoli rettangoli'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-8773577264441671144</id><published>2016-03-13T16:21:00.000-07:00</published><updated>2016-03-13T16:31:31.523-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Geometria del piano"/><category scheme="http://www.blogger.com/atom/ns#" term="medie"/><title type='text'>GEOMETRIA PIANA. Triangoli qualsiasi</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
659. <table align="center" border="0" cellpadding="5" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
660. <tr valign="top"><td style="font-size: 0.9em;" width="50%"><table border="0" cellpadding="3" cellspacing="0" class="cornice" style="border: 1px solid rgb(238, 238, 238); line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
661. <tr><td style="font-size: 0.9em;"><span style="color: #0b5394;">Il tuo browser non visualizza le applet Java.<br />Sul computer che utilizzi deve essere installata la Java Virtual Machine, in una versione 1.4 o successiva.</span></td></tr>
662. <tr><td class="nota" style="color: #777777; font-size: 0.9em; line-height: 1.3em;"><span style="color: #0b5394;">Prova a muovere i vertici del triangolo per vedere come variano i suoi elementi.</span></td></tr>
663. </tbody></table>
664. </td><td style="font-size: 0.9em;" width="50%"><b><span style="color: #0b5394;">LEGENDA</span></b><br />
665. <span style="color: #0b5394;">AB = <i>c</i>, AC = <i>b</i>, BC = <i>a </i>BAC = a, ABC = b, ACB = g<br /><b>AH</b> = <i>h</i>, altezza<br /><b>AM</b> = <i>m</i>, mediana<br /><b>AI</b> = <i>l</i>, bisettrice<br /><b>AD</b> = bisettrice angolo esterno<br /><i>p</i> = ½(<i>a</i> + <i>b</i> + <i>c</i>), semiperimetro<br /><i>A </i>= area</span><br />
666. <br />
667. <span style="color: #0b5394;"><img alt="indicatore" class="img-middle" height="9" src="http://www.math.it/images/frecver.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="9" /><a href="http://www.math.it/formulario/triangoloretto.htm" style="text-decoration: none;"> Vedi anche: triangoli rettangoli</a></span></td></tr>
668. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
669. <span style="color: #0b5394;"><b>» </b><b>Proprietà</b>:</span></div>
670. <span style="color: #0b5394;"><img alt="formula" height="26" src="http://www.math.it/formulario/images/triangolo/Image607.gif" width="117" /> , <img alt="formula" height="26" src="http://www.math.it/formulario/images/triangolo/Image608.gif" width="118" /> , <img alt="formula" height="26" src="http://www.math.it/formulario/images/triangolo/Image609.gif" width="118" /><br /><img alt="formula" height="21" src="http://www.math.it/formulario/images/triangolo/Image610.gif" width="102" /><br /><img alt="formula" height="21" src="http://www.math.it/formulario/images/triangolo/Image611.gif" width="93" /></span></td></tr>
671. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
672. <span style="color: #0b5394;"><b>» </b><b>Calcolo dell'area</b>:</span></div>
673. <span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image612.gif" width="59" /><br /><img alt="formula" class="img-middle" height="26" src="http://www.math.it/formulario/images/triangolo/Image613.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="207" /> formula di Erone<br /><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image614.gif" width="257" /><br /><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image615.gif" width="153" /><br /><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image616.gif" width="162" /></span><br />
674. <span style="color: #0b5394;">Note le coordinate dei tre vertici P<sub>1</sub>(x<sub>1</sub>;y<sub>1</sub>), P<sub>2</sub>(x<sub>2</sub>;y<sub>2</sub>), P<sub>3</sub>(x<sub>3</sub>;y<sub>3</sub>), l’Area si calcola con il determinante:<br /><img alt="formula" class="img-middle" height="74" src="http://www.math.it/formulario/images/triangolo/Image658.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="149" /></span></td></tr>
675. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
676. <span style="color: #0b5394;"><b>» </b><b>Lunghezza delle mediane</b>:</span></div>
677. <span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image617.gif" width="161" /> , <img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image618.gif" width="159" /> , <img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image619.gif" width="159" /></span></td></tr>
678. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
679. <span style="color: #0b5394;"><b>» </b><b class="evidenziato" style="letter-spacing: 0.1em;">Teorema della mediana</b>:</span></div>
680. <span style="color: #0b5394;"><img alt="formula" height="29" src="http://www.math.it/formulario/images/triangolo/Image621.gif" width="196" /></span></td></tr>
681. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
682. <span style="color: #0b5394;"><b>» </b><b class="evidenziato" style="letter-spacing: 0.1em;">Bisettrici</b>:</span></div>
683. <span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image622.gif" width="183" /> , <img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image623.gif" width="183" /> , <img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image624.gif" width="183" /><br /><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image625.gif" width="111" /> , <img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image626.gif" width="113" /> , <img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image627.gif" width="110" /></span></td></tr>
684. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
685. <span style="color: #0b5394;"><b>» </b><b>Teorema della bisettrice dell'angolo interno</b>:</span></div>
686. <span style="color: #0b5394;"><img alt="formula" height="18" src="http://www.math.it/formulario/images/triangolo/Image628.gif" width="121" /></span></td></tr>
687. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
688. <span style="color: #0b5394;"><b>» </b>Teorema della bisettrice dell'angolo esterno:</span></div>
689. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="18" src="http://www.math.it/formulario/images/triangolo/Image629.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="130" /> (se i segmenti esistono)</span></td></tr>
690. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
691. <span style="color: #0b5394;"><b>» </b>Raggio della circonferenza circoscritta:</span></div>
692. <span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image630.gif" width="62" /> ,<br /><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image631.gif" width="85" /> , <img alt="formula" height="43" src="http://www.math.it/formulario/images/triangolo/Image632.gif" width="83" /> , <img alt="formula" height="43" src="http://www.math.it/formulario/images/triangolo/Image633.gif" width="83" /></span></td></tr>
693. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
694. <span style="color: #0b5394;"><b>» </b>Raggio della circonferenza inscritta:</span></div>
695. <span style="color: #0b5394;"><img alt="formula" height="43" src="http://www.math.it/formulario/images/triangolo/Image634.gif" width="42" /> , <img alt="formula" height="49" src="http://www.math.it/formulario/images/triangolo/Image635.gif" width="189" /> ,<br /><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image636.gif" width="109" /> , <img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image637.gif" width="110" /> , <img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image638.gif" width="106" /></span></td></tr>
696. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
697. <span style="color: #0b5394;"><b>» </b>Raggio delle circonferenze exinscritte:</span></div>
698. <span style="color: #0b5394;"><img alt="formula" height="49" src="http://www.math.it/formulario/images/triangolo/Image639.gif" width="162" /> , <img alt="formula" height="49" src="http://www.math.it/formulario/images/triangolo/Image640.gif" width="162" /> , <img alt="formula" height="49" src="http://www.math.it/formulario/images/triangolo/Image641.gif" width="162" /></span><br />
699. <span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image642.gif" width="82" /> , <img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image643.gif" width="83" /> , <img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image644.gif" width="79" /></span></td></tr>
700. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
701. <span style="color: #0b5394;"><b>» </b>Altezze:</span></div>
702. <span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image645.gif" width="273" /> ,<br /><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image646.gif" width="271" /> ,<br /><img alt="formula" height="41" src="http://www.math.it/formulario/images/triangolo/Image647.gif" width="271" /></span></td></tr>
703. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
704. <span style="color: #0b5394;"><b>» </b>Teorema dei seni (o di Eulero)</span></div>
705. <span style="color: #0b5394;">In un triangolo è <i>costante</i> il rapporto tra la misura di un lato e il seno dell'angolo opposto:<br /><img alt="formula" height="43" src="http://www.math.it/formulario/images/triangolo/Image648.gif" width="144" /></span></td></tr>
706. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
707. <span style="color: #0b5394;"><b>» </b>Teorema della corda</span></div>
708. <div class="dividisopra" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px;">
709. <span style="color: #0b5394;">In un triangolo il rapporto tra la misura di un lato e il seno dell'angolo opposto è uguale al diametro della circonferenza circoscritta:<br /><img alt="formula" class="img-middle" height="43" src="http://www.math.it/formulario/images/triangolo/Image648.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="144" /> = <i>2r</i></span></div>
710. </td></tr>
711. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
712. <span style="color: #0b5394;"><b>» </b>Teorema delle proiezioni:</span></div>
713. <span style="color: #0b5394;">In un triangolo qualunque, la misura di un lato è uguale alla somma dei prodotti delle misure di ciascuno degli altri due per il coseno degli angoli che essi formano con il primo.</span><br />
714. <span style="color: #0b5394;"><img alt="formula" height="21" src="http://www.math.it/formulario/images/triangolo/Image652.gif" width="145" /> , <img alt="formula" height="21" src="http://www.math.it/formulario/images/triangolo/Image653.gif" width="144" /> , <img alt="v" height="21" src="http://www.math.it/formulario/images/triangolo/Image654.gif" width="145" /></span></td></tr>
715. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
716. <span style="color: #0b5394;"><b>» </b>Teorema del coseno (o di Carnot)</span></div>
717. <span style="color: #0b5394;">In un triangolo il quadrato di un lato è uguale alla somma dei quadrati degli altri due diminuita del prodotto di questi due lati per il coseno dell'angolo fra essi compreso:</span><br />
718. <span style="color: #0b5394;"><img alt="formula" height="25" src="http://www.math.it/formulario/images/triangolo/Image649.gif" width="168" /> , <img alt="formula" height="25" src="http://www.math.it/formulario/images/triangolo/Image650.gif" width="170" /> , <img alt="formula" height="25" src="http://www.math.it/formulario/images/triangolo/Image651.gif" width="168" />.</span></td></tr>
719. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
720. <b><span style="color: #0b5394;"><b>» </b>Formule di Briggs:</span></b></div>
721. <span style="color: #0b5394;"><img alt="formula" height="46" src="http://www.math.it/formulario/images/triangolo/Image655.gif" width="166" /> , <img alt="formula" height="46" src="http://www.math.it/formulario/images/triangolo/Image656.gif" width="169" /> , <img alt="formula" height="46" src="http://www.math.it/formulario/images/triangolo/Image657.gif" width="166" /><br /><img alt="formula" height="49" src="http://www.math.it/formulario/images/triangolo/Image436.gif" width="134" /> , <img alt="formula" height="49" src="http://www.math.it/formulario/images/triangolo/Image437.gif" width="136" />, <img alt="formula" height="49" src="http://www.math.it/formulario/images/triangolo/Image438.gif" width="132" /><br /><img alt="formula" height="54" src="http://www.math.it/formulario/images/triangolo/Image439.gif" width="160" /> , <img alt="formula" height="54" src="http://www.math.it/formulario/images/triangolo/Image440.gif" width="161" />, <img alt="formula" height="54" src="http://www.math.it/formulario/images/triangolo/Image441.gif" width="160" /><br /><img alt="formula" height="54" src="http://www.math.it/formulario/images/triangolo/Image442.gif" width="166" />, <img alt="formula" height="54" src="http://www.math.it/formulario/images/triangolo/Image443.gif" width="169" />, <img alt="formula" height="54" src="http://www.math.it/formulario/images/triangolo/Image444.gif" width="166" /></span></td></tr>
722. <tr valign="top"><td class="dividisopra" colspan="2" style="border-top-color: rgb(102, 0, 102); border-top-style: solid; border-top-width: 1px; font-size: 0.9em;"><div class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">
723. <span style="color: #0b5394;"><b>» </b>Teorema delle tangenti (o di <i>Nepero</i>)</span></div>
724. <span style="color: #0b5394;">In un triangolo qualsiasi la somma di due lati sta alla loro differenza come la tangente della semisomma degli angoli opposti ai suddetti lati sta alla tangente della loro semidifferenza:</span><br />
725. <span style="color: #0b5394;"><img alt="formula" height="80" src="http://www.math.it/formulario/images/triangolo/Image445.gif" width="110" /><br />che si può anche scrivere: <img alt="formula" class="img-middle" height="80" src="http://www.math.it/formulario/images/triangolo/Image446.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="109" /></span></td></tr>
726. </tbody></table>
727. </div>
728. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/8773577264441671144/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-piana-triangoli-qualsiasi.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/8773577264441671144'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/8773577264441671144'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/geometria-piana-triangoli-qualsiasi.html' title='GEOMETRIA PIANA. Triangoli qualsiasi'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-867005685686612874</id><published>2016-03-13T12:04:00.002-07:00</published><updated>2016-03-13T12:53:42.573-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="algebra"/><category scheme="http://www.blogger.com/atom/ns#" term="matematica"/><title type='text'>determinante di una matrice quadrata. Regola di Sarrus</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
729. <table align="center" border="0" cellpadding="5" cellspacing="5" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
730. <tr valign="top"><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><b>» </b>Definizione di <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;"><b>matrice</b></span></span><br />
731. <span style="color: #0b5394;">Un insieme di numeri ordinati secondo righe e colonne è detto <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;"><em>matrice</em></span> di ordine <em><b>m</b></em> x <em><b>n</b></em>, ove <em>m</em> è il numero delle righe e <em>n</em> il numero delle colonne.</span><br />
732. <span style="color: #0b5394;">Una <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;"><em>matrice</em></span> si dice <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;"><em>quadrata</em></span> se <img alt="m=n" class="img-middle" height="14" src="http://www.math.it/formulario/images/determinanti/Image370.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="41" />.</span><br />
733. <span style="color: #0b5394;">Il generico <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;"><i>elemento</i></span> della <i>matrice</i> <img alt="matrice Aij" class="img-middle" height="24" src="http://www.math.it/formulario/images/determinanti/Image371.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="29" /> si indica con <img alt="aij" class="img-middle" height="25" src="http://www.math.it/formulario/images/determinanti/Image372.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="24" />. Esso occupa la posizione individuata dall'intersezione tra la <em>i-esima</em> riga e la <em>j-esima</em> colonna della matrice.</span><br />
734. <span style="color: #0b5394;"><img alt="matrice" height="146" src="http://www.math.it/formulario/images/determinanti/Image373.gif" width="321" />, con <img align="absmiddle" alt="indici" height="48" src="http://www.math.it/formulario/images/determinanti/Image374.gif" width="123" /></span><br />
735. <span style="color: #0b5394;">La <b>teoria dei <em>DETERMINANTI</em></b> è stata sviluppata per poter risolvere i sistemi di equazioni lineari e trovare l'inversa di una matrice quadrata. Per questo fine è stato necessario associare ad ogni matrice quadrata un valore numerico. Tale numero è il <i>determinante della matrice</i>.</span><br />
736. <span style="color: #0b5394;">Ad ogni matrice quadrata <i>A</i> di ordine <i>n</i> può essere associato un numero che si chiama il suo determinante e si indica con <i>det A.</i></span></td></tr>
737. <tr valign="top"><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;"><strong>» </strong><b>Determinante di matrici quadrate del secondo ordine</b></span><span style="color: #0b5394;">Il <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;"><em>determinante</em></span><em> di una matrice quadrata del <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">secondo ordine</span></em> (2 righe e 2 colonne) <img alt="matrice" class="img-middle" height="50" src="http://www.math.it/formulario/images/determinanti/Image375.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="103" /> si calcola:<br /><img alt="determinante secondo ordine" class="img-middle" height="50" src="http://www.math.it/formulario/images/determinanti/Image376.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="240" /><br />Il <em>determinante di una matrice quadrata del secondo ordine</em> è uguale alla differenza dei prodotti degli elementi delle due diagonali (principale meno secondaria).</span></td></tr>
738. <tr valign="top"><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;" width="50%"><b><span style="color: #0b5394;"><b>» </b>Determinante di matrici quadrate del terzo ordine</span></b><br />
739. <span style="color: #0b5394;">Il calcolo del <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;"><em>determinante</em></span><em> di una matrice quadrata del <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">terzo ordine</span></em> (3 righe e 3 colonne) <img alt="matrice" class="img-middle" height="74" src="http://www.math.it/formulario/images/determinanti/Image377.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="139" /> si sviluppa secondo gli elementi di una riga o di una colonna. Nell'esempio sviluppiamo secondo la prima riga.<i><br /><img alt="determinante terzo ordine" height="74" src="http://www.math.it/formulario/images/determinanti/Image378.gif" width="463" />.</i></span><br />
740. <span style="color: #0b5394;">Ogni elemento della prima riga viene moltiplicato con il suo <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;"><em>MINORE COMPLEMENTARE</em></span>, ovvero il determinante del secondo ordine ottenuto sopprimendo la prima riga e la prima colonna; i prodotti vengono poi sommati algebricamente tra loro considerando il segno positivo se la somma degli indici dell'elemento considerato è pari, o negativo se è dispari.</span><br />
741. <span style="color: #0b5394;">Sviluppando i tre determinanti del secondo ordine, si ottiene:</span><br />
742. <i><span style="color: #0b5394;"><img alt="determinante terzo ordine" height="74" src="http://www.math.it/formulario/images/determinanti/Image379.gif" width="590" />.</span></i><br />
743. <span style="color: #0b5394;">È utile notare che il determinante di una matrice quadrata non cambia se lo sviluppo viene eseguito rispetto ad una qualsiasi altra riga (non solo la prima) o un'altra colonna.</span></td></tr>
744. <tr valign="top"><td class="dividisotto" style="border-bottom-color: rgb(102, 0, 102); border-bottom-style: solid; border-bottom-width: 1px; font-size: 0.9em;"><span style="color: #0b5394;">Un <b>secondo metodo</b> per il calcolo dei <em>determinanti del terzo ordine</em> è indicato dalla<i> <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;"><b>REGOLA DI SARRUS</b></span></i><strong>.</strong>Per la sua applicazione è conveniente disporre, accanto alla matrice data, copia delle prime due colonne ed eseguire i prodotti indicati, presi in segno positivo seguendo le frecce rosse e negativi seguendo le frecce blu.</span><br />
745. <span style="color: #0b5394;"><img alt="determinante Regola di Sarrus" height="128" src="http://www.math.it/formulario/images/determinanti/Image381.gif" width="375" /> </span><br />
746. <span style="color: #0b5394;"><img alt="determinante Regola di Sarrus" height="74" src="http://www.math.it/formulario/images/determinanti/Image382.gif" width="590" /></span></td></tr>
747. <tr valign="top"><td style="font-size: 0.9em;"><b><span style="color: #0b5394;"><b>» </b>Principali <span class="evidenziato" style="background-color: #eeeeee; letter-spacing: 0.1em;">proprietà</span></span></b><span style="color: #0b5394;">i) il valore di un determinante non cambia se si scambiano le righe con le colonne:</span><br />
748. <blockquote>
749. <span style="color: #0b5394;"><img alt="determinanti proprietà" height="74" src="http://www.math.it/formulario/images/determinanti/Image383.gif" width="217" /></span></blockquote>
750. <span style="color: #0b5394;">ii) lo scambio di due righe o di due colonne di un determinante equivale a cambiarne il segno, ovvero a moltiplicarlo per -1 :</span><br />
751. <blockquote>
752. <span style="color: #0b5394;"><img alt="determinanti proprietà" height="74" src="http://www.math.it/formulario/images/determinanti/Image384.gif" width="238" /></span></blockquote>
753. <span style="color: #0b5394;">iii) moltiplicare tutti gli elementi di una riga o di una colonna per uno stesso numero <i>k</i> equivale a moltiplicare il determinante per <i>k</i> :</span><br />
754. <blockquote>
755. <span style="color: #0b5394;"><img alt="determinanti proprietà" height="74" src="http://www.math.it/formulario/images/determinanti/Image385.gif" width="288" /></span></blockquote>
756. <span style="color: #0b5394;">iv) se tutti gli elementi di una riga o di una colonna sono nulli, il valore del determinante è nullo:</span><br />
757. <blockquote>
758. <span style="color: #0b5394;"><img alt="determinanti proprietà" height="74" src="http://www.math.it/formulario/images/determinanti/Image386.gif" width="117" /></span></blockquote>
759. </td></tr>
760. </tbody></table>
761. </div>
762. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/867005685686612874/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/determinante-di-una-matrice-quadrata.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/867005685686612874'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/867005685686612874'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/determinante-di-una-matrice-quadrata.html' title='determinante di una matrice quadrata. Regola di Sarrus'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-1907546134434640371</id><published>2016-03-13T12:03:00.006-07:00</published><updated>2016-03-13T12:53:42.536-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="algebra"/><category scheme="http://www.blogger.com/atom/ns#" term="matematica"/><title type='text'>logaritmi</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
763. <table border="0" cellpadding="3" cellspacing="3" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%%px;"><tbody>
764. <tr valign="top"><td style="font-size: 0.9em;" width="50%"><span style="color: #0b5394;"><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;"><b>definizione</b></span>:</span><br />
765. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="26" src="http://www.math.it/formulario/images/logaritmi/Image476.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="137" />, <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/logaritmi/Image477.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="169" /></span><br />
766. <b><span style="color: #0b5394;"><b>» </b><span class="evidenziato" style="background-color: #eeeeee; letter-spacing: 0.1em;">proprietà</span>:</span></b><br />
767. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="24" src="http://www.math.it/formulario/images/logaritmi/Image478.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="187" />, <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/logaritmi/Image479.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="161" /><br /><img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/logaritmi/Image480.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="165" />, <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/logaritmi/Image479.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="161" /><br /><img alt="formula" class="img-middle" height="26" src="http://www.math.it/formulario/images/logaritmi/Image481.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="134" />, <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/logaritmi/Image482.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="163" /><br /><img alt="formula" class="img-middle" height="41" src="http://www.math.it/formulario/images/logaritmi/Image483.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="139" />, <img alt="formula" class="img-middle" height="24" src="http://www.math.it/formulario/images/logaritmi/Image484.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="171" /></span></td><td style="font-size: 0.9em;" width="50%"><span style="color: #0b5394;"><b>» </b><span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;"><b>cambiamento di base</b></span>:</span><br />
768. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="46" src="http://www.math.it/formulario/images/logaritmi/Image485.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="102" />, <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/logaritmi/Image486.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="194" /></span></td></tr>
769. </tbody></table>
770. </div>
771. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/1907546134434640371/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/logaritmi.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/1907546134434640371'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/1907546134434640371'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/logaritmi.html' title='logaritmi'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-3630881227147763816</id><published>2016-03-13T12:03:00.002-07:00</published><updated>2016-03-13T12:53:42.554-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="algebra"/><category scheme="http://www.blogger.com/atom/ns#" term="matematica"/><title type='text'>disequazioni irrazionali</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
772. <table border="0" cellpadding="3" cellspacing="0" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
773. <tr valign="top"><td class="divididestra" rowspan="2" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;" width="48%"><span style="color: #0b5394;">Equazioni irrazionali</span><br />
774. <span style="color: #0b5394;"><img alt="" class="img-middle" height="29" src="http://www.math.it/formulario/images/disequazioni_irraz/image002.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="100" /></span><br />
775. <span style="color: #0b5394;"><img alt="" class="img-middle" height="33" src="http://www.math.it/formulario/images/disequazioni_irraz/image004.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="110" />                    se <em>n</em> è dispari</span><br />
776. <span style="color: #0b5394;"><img alt="" class="img-middle" height="85" src="http://www.math.it/formulario/images/disequazioni_irraz/image006.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="109" />                     se <em>n</em> è pari</span><br />
777. </td><td rowspan="2" style="font-size: 0.9em;" width="2%"><span style="color: #0b5394;"> </span></td><td style="font-size: 0.9em;" width="50%"><span style="color: #0b5394;">Disequazioni irrazionali</span><br />
778. <span style="color: #0b5394;">1° caso                        <img alt="" class="img-middle" height="28" src="http://www.math.it/formulario/images/disequazioni_irraz/image008.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="96" /></span><br />
779. <span style="color: #0b5394;"><img alt="" class="img-middle" height="29" src="http://www.math.it/formulario/images/disequazioni_irraz/image010.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="108" />                                           se <em>n</em> è dispari</span><br />
780. <span style="color: #0b5394;"> le soluzioni si ottengono imponendo e risolvendo i due sistemi</span><br />
781. <span style="color: #0b5394;"><img alt="" class="img-middle" height="51" src="http://www.math.it/formulario/images/disequazioni_irraz/image012.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="213" />                  se <em>n</em> è pari</span><br />
782. </td></tr>
783. <tr valign="top"><td style="font-size: 0.9em;"><span style="color: #0b5394;">2° caso                        <img alt="" class="img-middle" height="28" src="http://www.math.it/formulario/images/disequazioni_irraz/image014.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="96" />   </span><br />
784. <span style="color: #0b5394;"><img alt="" class="img-middle" height="27" src="http://www.math.it/formulario/images/disequazioni_irraz/image016.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="100" />                                  se <em>n</em> è dispari</span><br />
785. <span style="color: #0b5394;">le soluzioni si ottengono imponendo e risolvendo il sistema</span><br />
786. <span style="color: #0b5394;"> <img alt="" class="img-middle" height="77" src="http://www.math.it/formulario/images/disequazioni_irraz/image018.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="111" />                              se <em>n</em> è pari</span></td></tr>
787. </tbody></table>
788. </div>
789. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/3630881227147763816/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/disequazioni-irrazionali.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/3630881227147763816'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/3630881227147763816'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/disequazioni-irrazionali.html' title='disequazioni irrazionali'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-6749100220509682424.post-2702978713655106426</id><published>2016-03-13T12:02:00.003-07:00</published><updated>2016-03-13T12:53:42.549-07:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="algebra"/><category scheme="http://www.blogger.com/atom/ns#" term="matematica"/><title type='text'>equazione algebrica di secondo grado</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
790. <table border="0" cellpadding="5" cellspacing="5" style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 19.2px; line-height: 1.2em; margin: 0px; padding: 5px; width: 100%px;"><tbody>
791. <tr valign="top"><td class="divididestra" style="border-right-color: rgb(102, 0, 102); border-right-style: solid; border-right-width: 1px; font-size: 0.9em;" width="50%"><span style="color: #0b5394;">Un equazione algebrica di 2° grado si presenta nella forma: <img alt="equazione" class="img-middle" height="25" src="http://www.math.it/formulario/images/equazioni2/Image442.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="153" />.</span><br />
792. <span style="color: #0b5394;"><b>» </b>Se <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/equazioni2/Image443.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="77" /> l'equazione si dice in <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">forma completa</span> e si risolve utilizzando la <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;"><b>formula risolutiva</b></span>:<br /><img alt="formula risolutiva eq. secondo grado" height="48" src="http://www.math.it/formulario/images/equazioni2/Image444.gif" width="149" /></span><br />
793. <blockquote>
794. <span style="color: #0b5394;"><img alt="discriminante" class="img-middle" height="22" src="http://www.math.it/formulario/images/equazioni2/Image445.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="87" /> si dice <i>discriminante</i>;</span></blockquote>
795. <ul>
796. <li style="line-height: 1.8em; list-style-type: square; margin-left: 1em; padding: 0px;"><span style="color: #0b5394;">se <img alt="discriminante" class="img-middle" height="22" src="http://www.math.it/formulario/images/equazioni2/Image445.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="87" /> > 0 esistono <b>due soluzioni reali e distinte</b> che si ottengono applicando la <i>formula risolutiva</i></span></li>
797. <li style="line-height: 1.8em; list-style-type: square; margin-left: 1em; padding: 0px;"><span style="color: #0b5394;">se <img alt="discriminante" class="img-middle" height="22" src="http://www.math.it/formulario/images/equazioni2/Image445.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="87" /> = 0 esistono <b>due soluzioni reali e coincidenti</b> <img alt="soluzioni" class="img-middle" height="41" src="http://www.math.it/formulario/images/equazioni2/Image446.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="99" /></span></li>
798. <li style="line-height: 1.8em; list-style-type: square; margin-left: 1em; padding: 0px;"><span style="color: #0b5394;">se <img alt="discriminante" class="img-middle" height="22" src="http://www.math.it/formulario/images/equazioni2/Image445.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="87" /> < 0 esistono <b>due soluzioni complesse e coniugate.</b></span></li>
799. </ul>
800. <span style="color: #0b5394;"><b>» </b>Se <img alt="soluzioni" class="img-middle" height="21" src="http://www.math.it/formulario/images/equazioni2/Image447.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="77" /> l'equazione si dice <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">pura</span> e diventa <img alt="soluzioni" class="img-middle" height="22" src="http://www.math.it/formulario/images/equazioni2/Image448.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="75" />.<br />Le due soluzioni sono <img alt="soluzioni" class="img-middle" height="46" src="http://www.math.it/formulario/images/equazioni2/Image449.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="78" /></span><br />
801. <span style="color: #0b5394;"><b>» </b>Se <img alt="formula" class="img-middle" height="21" src="http://www.math.it/formulario/images/equazioni2/Image450.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="77" /> l' equazione si dice <span class="evidenziato" style="background-color: #eeeeee; font-weight: bold; letter-spacing: 0.1em;">spuria</span> e si risolve raccogliendo <img alt="formula" class="img-middle" height="26" src="http://www.math.it/formulario/images/equazioni2/Image451.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="88" /> per cui le soluzioni sono <img alt="soluzioni" class="img-middle" height="41" src="http://www.math.it/formulario/images/equazioni2/Image452.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="102" /></span></td><td style="font-size: 0.9em;" width="50%"><b><span style="color: #0b5394;"><b>» </b><span class="evidenziato" style="background-color: #eeeeee; letter-spacing: 0.1em;">Formula ridotta</span></span></b><br />
802. <span style="color: #0b5394;">Se <i>b</i> è pari, può essere più comodo applicare la formula risolutiva ridotta:<br /><img alt="formula ridotta risolutiva eq. secondo grado" height="73" src="http://www.math.it/formulario/images/equazioni2/Image453.gif" width="162" /></span><br />
803. <b><span style="color: #0b5394;"><b>» </b>Relazione tra le soluzioni e i coefficienti <i>a, b, c</i> dell'equazione:</span></b><br />
804. <span style="color: #0b5394;"><img alt="formula" height="41" src="http://www.math.it/formulario/images/equazioni2/Image454.gif" width="89" /> , <img alt="formula" height="41" src="http://www.math.it/formulario/images/equazioni2/Image455.gif" width="72" /></span><br />
805. <span style="color: #0b5394;"><img alt="formula" class="img-middle" height="25" src="http://www.math.it/formulario/images/equazioni2/Image456.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="186" /></span><br />
806. <b><span style="color: #0b5394;"><b>» </b>Scomposizione del trinomio di 2° grado:</span></b><br />
807. <span style="color: #0b5394;"><img alt="scomposizione" class="img-middle" height="25" src="http://www.math.it/formulario/images/equazioni2/Image457.gif" style="border: none; margin-bottom: 1px; margin-right: 1px; vertical-align: middle;" width="212" /></span></td></tr>
808. </tbody></table>
809. </div>
810. </content><link rel='replies' type='application/atom+xml' href='http://matematicasolo.blogspot.com/feeds/2702978713655106426/comments/default' title='Commenti sul post'/><link rel='replies' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/equazione-algebrica-di-secondo-grado.html#comment-form' title='0 Commenti'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/2702978713655106426'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/6749100220509682424/posts/default/2702978713655106426'/><link rel='alternate' type='text/html' href='http://matematicasolo.blogspot.com/2016/03/equazione-algebrica-di-secondo-grado.html' title='equazione algebrica di secondo grado'/><author><name>jonny</name><uri>http://www.blogger.com/profile/10108773898165712609</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='29' height='32' src='//blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW2vjTRdX4nKA7bPI97PdGFSxKxzZgwFk9AxLdqykjMdKDvejAEbap1YNhDEw02dKuKjbQOMV5hMY3Eq97OHvLQuvnx59EawK5QhIHZrlAOut6TbLuP2b_Nrc4Sac4z-A/s220/1231407127.jpg'/></author><thr:total>0</thr:total></entry></feed>

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