<!DOCTYPE html> <html xmlns="http://www.w3.org/1999/xhtml"><head> <!--[ GuppY v5.0.9 CeCILL Copyright (C) 2004-2014 by Laurent Duveau - http://www.freeguppy.org/ ]--> <meta http-equiv="content-type" content="text/html; charset=UTF-8"> <meta name="application-name" content="Casyopée - Paramètres géométriques dans les fonctions"> <title>Casyopée - Paramètres géométriques dans les fonctions</title> <meta name="description" content="Casyopée: a learning environment dedicated to functions"> <meta name="generator" content="GuppY CMS"> <meta name="author" content="lagrange"> <meta name="keywords" content="casyopée, functions, mathematics, geodynamic geometry, cas, symbolic computation,"> <meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1"> <meta name="apple-mobile-web-app-capable" content="yes"> <meta name="apple-mobile-web-app-status-bar-style" content="black"> <link rel="shortcut icon" href="https://casyopee.math.univ-paris-diderot.fr/guppy.ico"> <link rel="alternate" type="application/rss+xml" title="Casyopée : Actualité" hreflang="fr" href="https://casyopee.math.univ-paris-diderot.fr/data/fr-news.xml"> <link type="text/css" rel="stylesheet" href="skins/casyop/style.css"> <link type="text/css" rel="stylesheet" href="skins/casyop/jqstyle.css"> <style type="text/css" media="screen"> @import url(inc/auto.css); </style> <style type="text/css" media="print"> @import url(inc/print.css); </style> <link type="text/css" rel="stylesheet" href="inc/csshead/fotorama.css"> <link type="text/css" rel="stylesheet" href="inc/csshead/menubox.css"> <link type="text/css" rel="stylesheet" href="inc/csshead/slidesjs.css"> <script type="text/javascript"> //<![CDATA[ <!-- var charset = "UTF-8"; var site0 = "Casyopée"; var site3 = "https://casyopee.math.univ-paris-diderot.fr/"; var sValue = screen.width + "||" + screen.height + "||" + screen.availWidth + "||" + screen.availHeight; var today = new Date(), expires = new Date(); expires.setTime(today.getTime() + (365*24*60*60*1000)); document.cookie = "GuppYScreen" + "=" + encodeURIComponent(sValue) + ";expires=" + expires.toGMTString(); //--> //]]> </script> <script type="text/javascript" src="inc/hpage.js"></script> <script type="text/javascript" src="inc/jquery-min.js"></script> <script type="text/javascript" src="inc/jquery-migrate-min.js"></script> <script type="text/javascript" src="inc/jqscript.js"></script> <script type="text/javascript" src="inc/jshead/boxmenu_toggle.js"></script> <script type="text/javascript" src="inc/jshead/fotorama.js"></script> <script type="text/javascript" src="inc/jshead/jquery.imagecube.min.js"></script> <script type="text/javascript" src="inc/jshead/sidephoto.js"></script> <script type="text/javascript" src="inc/jshead/slides.min.jquery.js"></script> <script type="text/javascript" src="inc/jshead/slidesjs.js"></script> </head><body> <table style="margin: auto; width: 100%; text-align: center;"> <tbody> <tr> <td style="width: 100%; vertical-align: top;"> <div id="AboveBoxes"> </div> <br> <div class="tbl tblout" onmouseover="this.className = 'tbl tblover'" onmouseout="this.className = 'tbl tblout'"> <div style="padding: 6px;"> <h2>Paramètres géométriques dans les fonctions</h2> <p style="text-align: left;" class="MsoNormal">Dans Casyopée, les fonctions font le lien entre la géométrie et l algèbre. Ainsi, une fonction peut</p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">1. modéliser une dépendance entre grandeurs géométrique (une unité étant choisie, elle fait passer d une valeur de la première grandeur à la valeur correspondante de la seconde).</p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">2. être la fonction dont une droite donnée est la représentation graphique (modélisation d une droite).</p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">3. être la fonction dont le lieu d un point est la représentation graphique (modélisation d un lieu).</p> <h3>1. Un exemple de modélisation de dépendance avec «&nbsp;le triangle de Minh&nbsp;»</h3> <table class="MsoTableGrid" style="border: medium none currentcolor; border-collapse: collapse;" border="1" cellpadding="0" cellspacing="0"> <tbody> <tr style=""> <td style="border: 1pt solid windowtext; padding: 0cm 5.4pt; width: 284.4pt;" valign="top" width="379"> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">A sur l axe des x, O origine du repère, I sur l axe des y, OA=10, OI=5, M est un point libre sur [OA] et IMN est rectangle en M. Il s agit d étudier les variations de l aire du triangle MIN.</p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">Une fonction modèle est <sub><!--[if gte vml 1]><v:shape id="_x0000_i1028" type="#_x0000_t75" style='width:132pt;height:35.25pt'> <v:imagedata src="/help/imgFrModifHelp/image007.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrModifHelp/image008.jpg" v:shapes="_x0000_i1028" height="47" width="176"><!--[endif]--><o:p></o:p></sub></p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">Supposons maintenant que l on veuille étudier les variations pour une position quelconque du point I sur la droite. On redéfinit I comme point libre sur l axe des y.&nbsp; La fonction modèle&nbsp; depend alors de la position du point I</p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal"><sub><o:p></o:p></sub><img 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"><sub><o:p></o:p></sub></p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal"><font size="2">En tirant le Point I dans le volet Géométrie, on observe la déformation continue du graphe de la fonction modèle.</font><o:p></o:p></p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">En fait, la formule de la fonction modèle depend d'un parameter géométrique&nbsp;<i style=""><span style="font-family: Arial;">t<sub>I</sub></span></i>, représentant la position de I sur l axe des y. Il est possible de faire afficher ce parameter par le menu <span style="font-family: Arial; font-size: 10pt;">Options-Calcul et Justification- Instancier les paramètres géométriques.</span></p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal"><sub><!--[if gte vml 1]><v:shape id="_x0000_i1029" type="#_x0000_t75" style='width:195pt;height:63pt'> <v:imagedata src="/help/imgFrModifHelp/image009.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrModifHelp/image010.jpg" v:shapes="_x0000_i1029" height="84" width="260"><!--[endif]--><span style="">&nbsp;</span><o:p></o:p></sub></p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">Il est alors possible d'instancier explicitement les paramètres géométriques.:<o:p></o:p></p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal"><!--[if gte vml 1]><v:shape id="_x0000_i1030" type="#_x0000_t75" style='width:3in;height:27.75pt'> <v:imagedata src="/help/imgFrModifHelp/image011.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrModifHelp/image012.jpg" v:shapes="_x0000_i1030" height="37" width="288"><!--[endif]--></p> <p class="MsoNormal"><o:p>&nbsp;</o:p></p> </td> <td style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext currentcolor; border-width: 1pt 1pt 1pt medium; padding: 0cm 5.4pt; width: 202.7pt;" valign="top" width="270"> <p class="MsoNormal"><!--[if gte vml 1]><v:shape id="_x0000_i1031" type="#_x0000_t75" style='width:185.25pt;height:124.5pt' o:ole=""> <v:imagedata src="/help/imgFrModifHelp/image013.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrModifHelp/image014.jpg" v:shapes="_x0000_i1031" height="166" width="247"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1031" DrawAspect="Content" ObjectID="_1474121831"> </o:OLEObject> </xml><![endif]--><span style="">&nbsp;</span><!--[if gte vml 1]><v:shape id="_x0000_i1032" type="#_x0000_t75" style='width:210.75pt;height:129pt' o:ole=""> <v:imagedata src="/help/imgFrModifHelp/image015.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrModifHelp/image016.jpg" v:shapes="_x0000_i1032" height="172" width="281"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1032" DrawAspect="Content" ObjectID="_1474121833"> </o:OLEObject> </xml><![endif]--><span style="">&nbsp;</span><!--[if gte vml 1]><v:shape id="_x0000_i1033" type="#_x0000_t75" style='width:207.75pt;height:128.25pt' o:ole=""> <v:imagedata src="/help/imgFrModifHelp/image017.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrModifHelp/image018.jpg" v:shapes="_x0000_i1033" height="171" width="277"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1033" DrawAspect="Content" ObjectID="_1474121834"> </o:OLEObject> </xml><![endif]--></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><o:p>&nbsp;</o:p></p> <h3>2. "Equations" de droite</h3> <table class="MsoTableGrid" style="border: medium none currentcolor; border-collapse: collapse;" border="1" cellpadding="0" cellspacing="0"> <tbody> <tr style=""> <td style="border: 1pt solid windowtext; padding: 0cm 5.4pt; width: 243.55pt;" valign="top" width="325"> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">Le menu contextuel des droites donne accès à un menu <span style="font-family: Arial; font-size: 10pt;">Equation-Exporter comme fonction.<o:p></o:p></span></p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">La fonction affine obtenue a pour représentation graphique la droite.</p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">Ici la droite dépend des deux points libres I et M, et donc leurs paramètres sont dans la formule.</p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal"><!--[if gte vml 1]><v:shape id="_x0000_i1034" type="#_x0000_t75" style='width:108pt;height:33.75pt'> <v:imagedata src="/help/imgFrModifHelp/image019.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrModifHelp/image020.jpg" v:shapes="_x0000_i1034" height="45" width="144"><!--[endif]--></p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">Notez que par défaut les paramètres géométriques sont instanciés automatiquement.</p> </td> <td style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext currentcolor; border-width: 1pt 1pt 1pt medium; padding: 0cm 5.4pt; width: 243.55pt;" valign="top" width="325"> <p class="MsoNormal"><!--[if gte vml 1]><v:shape id="_x0000_i1035" type="#_x0000_t75" style='width:273pt;height:144.75pt' o:ole=""> <v:imagedata src="/help/imgFrModifHelp/image021.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrModifHelp/image022.jpg" v:shapes="_x0000_i1035" height="193" width="364"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1035" DrawAspect="Content" ObjectID="_1474121835"> </o:OLEObject> </xml><![endif]--></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><o:p>&nbsp;</o:p></p> <h3>3. Lieux géométriques</h3> <table class="MsoTableGrid" style="border: medium none currentcolor; border-collapse: collapse;" border="1" cellpadding="0" cellspacing="0"> <tbody> <tr style=""> <td style="border: 1pt solid windowtext; padding: 0cm 5.4pt; width: 248.4pt;" valign="top" width="331"> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">Dans les versions précédentes, il était possible d obtenir le lieu d un point seulement si celui-ci ne dépendait que d un seul paramètre de point libre (par exemple le paramètre d un point libre sur objet).</p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal"><span style="text-decoration: underline;">Exemple</span>&nbsp;: construction d une parabole par foyer et directrice</p> <div style="text-align: left;"> </div> <div style="border: 1pt solid windowtext; padding: 1pt 4pt; text-align: left;"> <p class="MsoNormal" style="border: medium none currentcolor; padding: 0cm;"><span style="font-family: Arial; font-size: 10pt;">Création du Point Libre p1 sur (oy) renommé en F<o:p></o:p></span></p> <p class="MsoNormal" style="border: medium none currentcolor; padding: 0cm;"><span style="font-family: Arial; font-size: 10pt;">Création du point p2 image du point F par la Symétrie de centre p0<o:p></o:p></span></p> <p class="MsoNormal" style="border: medium none currentcolor; padding: 0cm;"><span style="font-family: Arial; font-size: 10pt;">Création de la Droite Parallèle D2 à la Droite (ox) et passant par le point p2<o:p></o:p></span></p> <p class="MsoNormal" style="border: medium none currentcolor; padding: 0cm;"><span style="font-family: Arial; font-size: 10pt;">Création du Point Libre p3 sur D2 renommé en H<o:p></o:p></span></p> <p class="MsoNormal" style="border: medium none currentcolor; padding: 0cm;"><span style="font-family: Arial; font-size: 10pt;">Création de la Droite Parallèle D3 à la Droite (oy) et passant par le point H<o:p></o:p></span></p> <p class="MsoNormal" style="border: medium none currentcolor; padding: 0cm;"><span style="font-family: Arial; font-size: 10pt;">Création du Point Milieu p4 du Segment [FH]<o:p></o:p></span></p> <p class="MsoNormal" style="border: medium none currentcolor; padding: 0cm;"><span style="font-family: Arial; font-size: 10pt;">Création du Segment [FH]<o:p></o:p></span></p> <p class="MsoNormal" style="border: medium none currentcolor; padding: 0cm;"><span style="font-family: Arial; font-size: 10pt;">Création de la Droite Perpendiculaire D4 à la Droite [FH] et passant par le point p4<o:p></o:p></span></p> <p class="MsoNormal" style="border: medium none currentcolor; padding: 0cm;"><span style="font-family: Arial; font-size: 10pt;">Création du Point d'intersection<span style="">&nbsp; </span>des droites D4 et D3, p5 renommé en M<o:p></o:p></span></p> </div> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">Avec le bouton<!--[if gte vml 1]><v:shape id="_x0000_i1036" type="#_x0000_t75" style='width:30pt;height:24pt'> <v:imagedata src="/help/imgFrModifHelp/image023.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--> <img src="/help/imgFrModifHelp/image024.jpg" v:shapes="_x0000_i1036" height="32" width="40"><!--[endif]-->dans le menu des droites,<span style="font-family: Arial; font-size: 10pt;"> o</span>n clique sur M puis sur H, la fonction<!--[if gte vml 1]><v:shape id="_x0000_i1037" type="#_x0000_t75" style='width:78pt;height:42pt'> <v:imagedata src="/help/imgFrModifHelp/image025.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--> <img src="/help/imgFrModifHelp/image026.jpg" v:shapes="_x0000_i1037" height="56" width="104"><!--[endif]-->est créée et la parabole s affiche.</p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">En tirant le point F, on change l excentricité de la parabole.</p> <div style="text-align: left;"> </div> <p style="text-align: left;" class="MsoNormal">Notez que par défaut les paramètres géométriques sont instanciés automatiquement.</p> <p class="MsoNormal"><o:p>&nbsp;</o:p></p> </td> <td style="border-style: solid solid solid none; border-color: windowtext windowtext windowtext currentcolor; border-width: 1pt 1pt 1pt medium; padding: 0cm 5.4pt; width: 242.5pt;" valign="top" width="323"> <p class="MsoNormal"><!--[if gte vml 1]><v:shape id="_x0000_i1038" type="#_x0000_t75" style='width:229.5pt;height:192pt'> <v:imagedata src="/help/imgFrModifHelp/image027.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrModifHelp/image028.jpg" v:shapes="_x0000_i1038" height="256" width="306"><!--[endif]--><!--[if gte vml 1]><v:shape id="_x0000_i1039" type="#_x0000_t75" style='width:234pt;height:195.75pt'> <v:imagedata src="/help/imgFrModifHelp/image029.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrModifHelp/image030.jpg" v:shapes="_x0000_i1039" height="261" width="312"><!--[endif]--></p> </td> </tr> </tbody> </table> </div> </div></td></tr></tbody> </table> </body></html>