<!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 - Un problème d'optimisation"> <title>Casyopée - Un problème d'optimisation</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 auto auto 0px; width: 100%; text-align: left;"> <tbody> <tr> <td style="width: 100%; vertical-align: top;"> <div id="AboveBoxes"> </div> <!-- Begin of ABOVE_BOXES --> <div class="tbl tblout" onmouseover="this.className = 'tbl tblover'" onmouseout="this.className = 'tbl tblout'"> <div style="padding: 6px;"> <h1>Un problème d'optimisation</h1> <h3><a href="pg92.htm#cons">Construction</a></h3> <h3><a href="pg92.htm#_Toc364193850">Modélisation</a></h3> <h3><a href="pg92.htm#Anim">Animation</a></h3> <p class="MsoNormal">Nous étudions la dépendance entre un calcul géométrique et une variable géométrique en traitant un exemple d optimisation d une aire.<span style="">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></p> <div style="border: 1pt solid windowtext; padding: 1pt 4pt; margin-right: 94.3pt; margin-left: 77pt;"> <p class="MsoNormal" style="border: medium none currentcolor; padding: 0cm;">Un segment [OA] de longueur 10, un point M mobile sur ce segment, un point I sur la perpendiculaire en O à (OA), N le point sur la perpendiculaire en A à (OA) construit de façon que le triangle MIN soit rectangle en M. On cherche la (les) position(s) de M maximisant l aire du triangle.</p> </div> <h3 class="MsoNormal" style="page-break-after: avoid;"><o:p>&nbsp;<a id="cons" name="cons">Construction</a></o:p></h3> <table class="MsoTableGrid" style="width: 100%; border-collapse: collapse;" border="0" cellpadding="0" cellspacing="0" width="100%"> <tbody> <tr style=""> <td style="padding: 0cm 5.4pt; width: 34.1%;" width="34%"> <p class="MsoNormal">Nous nous plaçons dans le cas OI=5</p> <p class="MsoNormal">Le fonctionnement des boutons de construction est similaire à celui de GeoGebra. Chaque bouton donne accès à un ensemble de fonctions.</p> <p class="MsoNormal">On commencera par adapter l écran de géométrie avec le bouton servant à déplacer et à zoomer.</p> </td> <td style="padding: 0cm 5.4pt; width: 65.9%;" width="65%"> <p class="MsoNormal" style="text-align: center; text-indent: 36pt;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1144" type="#_x0000_t75" style='width:285.75pt;height:179.25pt' o:ole="" o:bordertopcolor="#36f" o:borderleftcolor="#36f" o:borderbottomcolor="#36f" o:borderrightcolor="#36f"> <v:imagedata src="/help/imgFrHelp/image209.png" o:title=""/> <w:bordertop type="single" width="12"/> <w:borderleft type="single" width="12"/> <w:borderbottom type="single" width="12"/> <w:borderright type="single" width="12"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image210.jpg" v:shapes="_x0000_i1144" border="0" height="243" width="385"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1144" DrawAspect="Content" ObjectID="_1473694197"> </o:OLEObject> </xml><![endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193844">Figure </a><!--[if supportFields]><span style='mso-bookmark:_Toc364193844'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193844'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">87</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193844'></span><span style='mso-element:field-end'></span><![endif]--><span style=""> : Zoom et déplacement</span></p> </td> </tr> <tr style=""> <td style="padding: 0cm 5.4pt; width: 34.1%;" width="34%"> <p class="MsoNormal">Ensuite, on crée une droite perpendiculaire à l axe des x au point de coordonnées (0, 10), puis le segment de l origine à ce point.</p> <p class="MsoNormal">Création de segment et de perpendiculaire sont sous le même bouton. Cliquez d abord sur l axe des x, puis à proximité du point de<span style="">&nbsp;&nbsp; </span>coordonnées (0, 10). Choisissez dans le menu comme indiqué sur la figure.</p> </td> <td style="padding: 0cm 5.4pt; width: 65.9%;" width="65%"> <p class="MsoCaption" style="text-align: center; page-break-after: avoid;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1145" type="#_x0000_t75" style='width:318pt;height:238.5pt' o:ole=""> <v:imagedata src="/help/imgFrHelp/image211.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image212.jpg" v:shapes="_x0000_i1145" border="0" height="318" width="424"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1145" DrawAspect="Content" ObjectID="_1473694198"> </o:OLEObject> </xml><![endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193845">Figure </a><!--[if supportFields]><span style='mso-bookmark:_Toc364193845'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193845'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">88</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193845'></span><span style='mso-element:field-end'></span><![endif]--><span style=""> : <span style="">&nbsp;</span>Création droite perpendiculaire</span></p> </td> </tr> <tr style=""> <td style="padding: 0cm 5.4pt; width: 34.1%;" width="34%"> <p class="MsoNormal">On crée de même un segment du point de coordonnées (5,0) vers un point libre sur le segment qui vient d être créé.</p> <p class="MsoNormal">Attention, il faut bien choisir le point dans le menu.</p> </td> <td style="padding: 0cm 5.4pt; width: 65.9%;" width="65%"> <p class="MsoNormal" style="text-align: center; text-indent: 36pt; page-break-after: avoid;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1146" type="#_x0000_t75" style='width:238.5pt;height:143.25pt' o:ole="" o:bordertopcolor="#36f" o:borderleftcolor="#36f" o:borderbottomcolor="#36f" o:borderrightcolor="#36f"> <v:imagedata src="/help/imgFrHelp/image213.png" o:title=""/> <w:bordertop type="single" width="12"/> <w:borderleft type="single" width="12"/> <w:borderbottom type="single" width="12"/> <w:borderright type="single" width="12"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image214.jpg" v:shapes="_x0000_i1146" border="0" height="195" width="322"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1146" DrawAspect="Content" ObjectID="_1473694199"> </o:OLEObject> </xml><![endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193846">Figure </a><!--[if supportFields]><span style='mso-bookmark:_Toc364193846'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193846'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">89</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193846'></span><span style='mso-element:field-end'></span><![endif]--><span style=""> : Création segment</span></p> </td> </tr> <tr style=""> <td style="padding: 0cm 5.4pt; width: 34.1%;" width="34%"> <p class="MsoNormal">On créée ensuite la perpendiculaire au segment passant par le point libre.</p> <p class="MsoNormal">Le bouton point permet de choisir le point d intersection voulu par un menu quand la souris est proche de cette intersection.</p> </td> <td style="padding: 0cm 5.4pt; width: 65.9%;" width="65%"> <p class="MsoNormal" style="text-align: center; text-indent: 36pt;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1147" type="#_x0000_t75" style='width:291.75pt;height:153.75pt' o:ole="" o:bordertopcolor="#36f" o:borderleftcolor="#36f" o:borderbottomcolor="#36f" o:borderrightcolor="#36f"> <v:imagedata src="/help/imgFrHelp/image215.png" o:title=""/> <w:bordertop type="single" width="12"/> <w:borderleft type="single" width="12"/> <w:borderbottom type="single" width="12"/> <w:borderright type="single" width="12"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image216.jpg" v:shapes="_x0000_i1147" border="0" height="209" width="393"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1147" DrawAspect="Content" ObjectID="_1473694200"> </o:OLEObject> </xml><![endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193847">Figure </a><!--[if supportFields]><span style='mso-bookmark:_Toc364193847'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193847'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">90</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193847'></span><span style='mso-element:field-end'></span><![endif]--><span style="">: création perpendiculaire vers un point libre</span></p> </td> </tr> <tr style=""> <td style="padding: 0cm 5.4pt; width: 34.1%;" width="34%"> <p class="MsoNormal">Le bouton polygone permet de créer un triangle en cliquant successivement sur chaque point.</p> <p class="MsoNormal">Il est temps de donner un nom aux points</p> <p class="MsoNormal">Ceci se fait en utilisant le menu contextuel (clic droit) de chaque objet.</p> </td> <td style="padding: 0cm 5.4pt; width: 65.9%;" width="65%"> <p class="MsoNormal" style="text-align: center; text-indent: 36pt;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1148" type="#_x0000_t75" style='width:290.25pt;height:191.25pt' o:ole="" o:bordertopcolor="#36f" o:borderleftcolor="#36f" o:borderbottomcolor="#36f" o:borderrightcolor="#36f"> <v:imagedata src="/help/imgFrHelp/image217.png" o:title=""/> <w:bordertop type="single" width="12"/> <w:borderleft type="single" width="12"/> <w:borderbottom type="single" width="12"/> <w:borderright type="single" width="12"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image218.jpg" v:shapes="_x0000_i1148" border="0" height="259" width="391"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1148" DrawAspect="Content" ObjectID="_1473694202"> </o:OLEObject> </xml><![endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193848">Figure </a><!--[if supportFields]><span style='mso-bookmark:_Toc364193848'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193848'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">91</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193848'></span><span style='mso-element:field-end'></span><![endif]--><span style=""> : Création triangle et nommage des points</span></p> <p class="MsoNormal" style="text-align: center; text-indent: 36pt;" align="center"><o:p>&nbsp;</o:p></p> </td> </tr> <tr style=""> <td style="padding: 0cm 5.4pt; width: 34.1%;" width="34%"> <p class="MsoNormal">On peut aussi créer des angles avec le même bouton que les polygones&nbsp;: on clique successivement trois points.</p> <p class="MsoNormal"><o:p>&nbsp;</o:p></p> </td> <td style="padding: 0cm 5.4pt; width: 65.9%;" width="65%"> <p class="MsoNormal" style="text-align: center; text-indent: 36pt; page-break-after: avoid;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1149" type="#_x0000_t75" style='width:243pt;height:222pt' o:ole="" o:bordertopcolor="#36f" o:borderleftcolor="#36f" o:borderbottomcolor="#36f" o:borderrightcolor="#36f"> <v:imagedata src="/help/imgFrHelp/image219.png" o:title=""/> <w:bordertop type="single" width="12"/> <w:borderleft type="single" width="12"/> <w:borderbottom type="single" width="12"/> <w:borderright type="single" width="12"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image220.jpg" v:shapes="_x0000_i1149" border="0" height="300" width="328"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1149" DrawAspect="Content" ObjectID="_1473694203"> </o:OLEObject> </xml><![endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193849">Figure </a><!--[if supportFields]><span style='mso-bookmark:_Toc364193849'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193849'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">92</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193849'></span><span style='mso-element:field-end'></span><![endif]--><span style="">: Création angles</span></p> </td> </tr> <tr style=""> <td style="padding: 0cm 5.4pt; width: 34.1%;" width="34%"> <p class="MsoNormal">Ici, les angles choisis sont codés comme des angles droits.</p> <p class="MsoNormal">On peut faire afficher certains éléments (aire, coordonnées) toujours en utilisant le menu contextuel.</p> </td> <td style="padding: 0cm 5.4pt; width: 65.9%;" width="65%"> <p class="MsoNormal" style="text-align: center; text-indent: 36pt;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1150" type="#_x0000_t75" style='width:240.75pt;height:163.5pt' o:ole="" o:bordertopcolor="#36f" o:borderleftcolor="#36f" o:borderbottomcolor="#36f" o:borderrightcolor="#36f"> <v:imagedata src="/help/imgFrHelp/image221.png" o:title=""/> <w:bordertop type="single" width="12"/> <w:borderleft type="single" width="12"/> <w:borderbottom type="single" width="12"/> <w:borderright type="single" width="12"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image222.jpg" v:shapes="_x0000_i1150" border="0" height="222" width="325"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1150" DrawAspect="Content" ObjectID="_1473694204"> </o:OLEObject> </xml><![endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193850">Figure </a><!--[if supportFields]><span style='mso-bookmark:_Toc364193850'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193850'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">93</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193850'></span><span style='mso-element:field-end'></span><![endif]--><span style="">: création d'une étiquette (aire)</span></p> </td> </tr> <tr style=""> <td style="padding: 0cm 5.4pt; width: 34.1%;" width="34%"> <h3 class="MsoNormal"><a id="Model" name="Model">Modélisation</a></h3> <p class="MsoNormal">Nous allons passer à la modélisation. Basculez dans le <i style="">volet de calculs géométriques</i> (bouton <sub><span style="line-height: 115%;"><!--[if gte vml 1]><v:shape id="_x0000_i1151" type="#_x0000_t75" style='width:108.75pt;height:17.25pt'> <v:imagedata src="/help/imgFrHelp/image013.jpg" o:title="bouton_calculs_geo"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image014.jpg" v:shapes="_x0000_i1151" border="0" height="23" width="145"><!--[endif]--></span></sub>)</p> <p class="MsoNormal">Nous devons créer des «&nbsp;calculs géométriques&nbsp;» pour la variable et la valeur de la fonction.<span style="line-height: 115%;"> Cliquez sur<sub><!--[if gte vml 1]><v:shape id="_x0000_i1152" type="#_x0000_t75" style='width:75.75pt;height:18.75pt'> <v:imagedata src="/help/imgFrHelp/image223.jpg" o:title="creer_calc"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image224.jpg" v:shapes="_x0000_i1152" border="0" height="25" width="101"><!--[endif]--></sub>. </span>Nous choisissons successivement la distance OM et une formule donnant l aire du triangle.</p> </td> <td style="padding: 0cm 5.4pt; width: 65.9%;" width="65%"> <p class="MsoNormal" style="text-align: center; text-indent: 36pt; page-break-after: avoid;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1153" type="#_x0000_t75" style='width:273.75pt;height:176.25pt' o:ole="" o:bordertopcolor="#36f" o:borderleftcolor="#36f" o:borderbottomcolor="#36f" o:borderrightcolor="#36f"> <v:imagedata src="/help/imgFrHelp/image225.png" o:title=""/> <w:bordertop type="single" width="12"/> <w:borderleft type="single" width="12"/> <w:borderbottom type="single" width="12"/> <w:borderright type="single" width="12"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image226.jpg" v:shapes="_x0000_i1153" border="0" height="239" width="369"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1153" DrawAspect="Content" ObjectID="_1473694205"> </o:OLEObject> </xml><![endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193851">Figure </a><!--[if supportFields]><span style='mso-bookmark:_Toc364193851'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193851'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">94</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193851'></span><span style='mso-element:field-end'></span><![endif]--><span style=""> : calcul géométrique</span></p> </td> </tr> <tr style=""> <td style="padding: 0cm 5.4pt; width: 34.1%;" width="34%"> <p class="MsoNormal">Casyopée leur donne les étiquettes c0 et c1.<br> Les valeurs numériques des calculs permettent de détecter d éventuelles erreurs dans la modélisation.</p> <p class="MsoNormal">Choisissons c0 et c1 dans les listes à droite du bouton&nbsp;<span style="background: silver none repeat scroll 0% 50%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">modéliser</span>.</p> </td> <td style="padding: 0cm 5.4pt; width: 65.9%;" width="65%"> <p class="MsoNormal" style="text-align: center; text-indent: 36pt; page-break-after: avoid;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1154" type="#_x0000_t75" style='width:282.75pt;height:198.75pt' o:ole=""> <v:imagedata src="/help/imgFrHelp/image227.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image228.jpg" v:shapes="_x0000_i1154" border="0" height="265" width="377"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1154" DrawAspect="Content" ObjectID="_1473694206"> </o:OLEObject> </xml><![endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193852">Figure </a><!--[if supportFields]><span style='mso-bookmark:_Toc364193852'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193852'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">95</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193852'></span><span style='mso-element:field-end'></span><![endif]--><span style=""> : modélisation</span></p> </td> </tr> <tr style=""> <td style="padding: 0cm 5.4pt; width: 34.1%;" width="34%"> <p class="MsoNormal">Le bouton «&nbsp;<span style="background: silver none repeat scroll 0% 50%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">modéliser</span>&nbsp;» donne accès à un menu où nous choisissons l entrée&nbsp;: <b style="">Table Valeurs<o:p></o:p></b></p> <p class="MsoNormal">Les valeurs prises par les deux calculs pour une série de positions du point M s affichent. Le bouton<!--[if gte vml 1]><v:shape id="_x0000_i1155" type="#_x0000_t75" style='width:32.25pt;height:17.25pt'> <v:imagedata src="/help/imgFrHelp/image108.gif" o:title=""/> </v:shape><![endif]--><!--[if !vml]--> <img src="/help/imgFrHelp/image108.gif" v:shapes="_x0000_i1155" border="0" height="23" width="43"><!--[endif]--><span style="">&nbsp;</span>permet de copier la table dans le presse-papier. Il est alors possible de coller les valeurs dans un traitement de texte ou un tableur.</p> <p class="MsoNormal">La visualisation graphique permet de conjecturer une dépendance fonctionnelle de c0 à c1. Nous allons modéliser algébriquement cette dépendance.</p> </td> <td style="padding: 0cm 5.4pt; width: 65.9%;" width="65%"> <p class="MsoNormal" style="text-align: center; text-indent: 36pt; page-break-after: avoid;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1156" type="#_x0000_t75" style='width:278.25pt;height:307.5pt' o:ole=""> <v:imagedata src="/help/imgFrHelp/image229.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image230.jpg" v:shapes="_x0000_i1156" border="0" height="410" width="371"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1156" DrawAspect="Content" ObjectID="_1473694208"> </o:OLEObject> </xml><![endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193853">Figure </a><!--[if supportFields]><span style='mso-bookmark:_Toc364193853'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193853'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">96</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193853'></span><span style='mso-element:field-end'></span><![endif]--><span style=""> : modéliser, table valeurs</span></p> </td> </tr> <tr style=""> <td style="padding: 0cm 5.4pt; width: 34.1%;" width="34%"> <p class="MsoNormal">Le bouton «&nbsp;<span style="background: silver none repeat scroll 0% 50%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">modéliser</span>&nbsp;» donne accès à un menu où nous choisissons l entrée&nbsp;: <b style="">calcul fonction modèle par Casyopée</b>. L ensemble de définition et une formule pour la fonction sont calculés par Casyopée. Il est important de cocher la case <span style="background: silver none repeat scroll 0% 50%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Vérification Existence</span>.</p> </td> <td style="padding: 0cm 5.4pt; width: 65.9%;" width="65%"> <p class="MsoNormal" style="text-align: center; text-indent: 36pt; page-break-after: avoid;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1157" type="#_x0000_t75" style='width:281.25pt;height:108pt' o:ole="" o:bordertopcolor="#36f" o:borderleftcolor="#36f" o:borderbottomcolor="#36f" o:borderrightcolor="#36f"> <v:imagedata src="/help/imgFrHelp/image231.png" o:title=""/> <w:bordertop type="single" width="12"/> <w:borderleft type="single" width="12"/> <w:borderbottom type="single" width="12"/> <w:borderright type="single" width="12"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image232.jpg" v:shapes="_x0000_i1157" border="0" height="148" width="379"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1157" DrawAspect="Content" ObjectID="_1473694209"> </o:OLEObject> </xml><![endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193854">Figure </a><!--[if supportFields]><span style='mso-bookmark:_Toc364193854'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193854'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">97</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193854'></span><span style='mso-element:field-end'></span><![endif]--><span style=""> : modéliser calcul fonction modèle par Casyopée.</span></p> </td> </tr> <tr style=""> <td style="padding: 0cm 5.4pt; width: 34.1%;" width="34%"> <p class="MsoNormal">Après acceptation des données, la fonction est créée dans le volet Algèbre. Le mini tableau s affiche car le domaine a été vérifié à l étape précédente. Il est alors très simple de prouver par une étude de variation aidée par Casyopée, des conjectures émises par observation sur la figure</p> </td> <td style="padding: 0cm 5.4pt; width: 65.9%;" width="65%"> <p class="MsoNormal" style="text-align: center; page-break-after: avoid;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1158" type="#_x0000_t75" style='width:282pt;height:108.75pt' o:ole="" o:bordertopcolor="#36f" o:borderleftcolor="#36f" o:borderbottomcolor="#36f" o:borderrightcolor="#36f"> <v:imagedata src="/help/imgFrHelp/image233.png" o:title=""/> <w:bordertop type="single" width="12"/> <w:borderleft type="single" width="12"/> <w:borderbottom type="single" width="12"/> <w:borderright type="single" width="12"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image234.gif" v:shapes="_x0000_i1158" border="0" height="149" width="380"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1158" DrawAspect="Content" ObjectID="_1473694210"> </o:OLEObject> </xml><![endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193855">Figure </a><!--[if supportFields]><span style='mso-bookmark:_Toc364193855'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193855'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">98</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193855'></span><span style='mso-element:field-end'></span><![endif]--><span style=""> : fonction modèle</span></p> <p class="MsoNormal">On conjecture puis on prouve deux maximas, l un quand M est en 0, l autre quand il est au milieu de [OA].</p> </td> </tr> <tr style=""> <td style="padding: 0cm 5.4pt; width: 34.1%;" width="34%"> <h3 class="MsoNormal" style="text-indent: 0.65pt;"><a id="Anim" name="Anim">Animation</a></h3> <p class="MsoNormal" style="text-indent: 0.65pt;"><span style="line-height: 115%;">Revenez au <i style="">volet de géométrie</i> (entrée de menu<sub><!--[if !vml]--><img src="/help/imgFrHelp/image010.jpg" v:shapes="_x0000_i1159" border="0" height="24" width="80"><!--[endif]--></sub>) et activez le <i style="">volet graphique</i> grâce à l entrée de menu<sub><!--[if gte vml 1]><v:shape id="_x0000_i1160" type="#_x0000_t75" style='width:63pt;height:21pt'> <v:imagedata src="/help/imgFrHelp/image015.jpg" o:title="bouton_graph"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image016.jpg" v:shapes="_x0000_i1160" border="0" height="28" width="84"><!--[endif]--></sub>. Il y a interaction entre la construction dans le <i style="">volet de géométrie dynamique</i> et les représentations des fonctions&nbsp;: pointez sur une des courbes du <i style="">volet graphique</i> avec la souris, déplacez le point M, le viseur (trace) se déplace en conséquence sur la courbe et les valeurs prises par la fonction s affichent. Pointez sur la courbe, déplacez<span style="">&nbsp; </span>le viseur sur cette courbe, le point M se déplace aussi. On peut aussi utiliser le curseur en bas du volet graphique.<o:p></o:p></span></p> <p class="MsoNormal"><span style="line-height: 115%;">Vous pouvez <b style="">Attacher une image</b></span> à des points (ici M et N). Une fois attachées, ces images pourront être déplacées relativement aux points. Pour créer une animation, donner une vitesse au point M (menu contextuel, <b style="">Propriétés</b>) et enregistrer l écran en GIF animé (menu <b style="">Fichiers</b>).</p> </td> <td style="padding: 0cm 5.4pt; width: 65.9%;" width="65%"> <p class="MsoNormal" style="text-align: center; text-indent: 36pt;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1161" type="#_x0000_t75" style='width:313.5pt;height:157.5pt' o:bordertopcolor="#36f" o:borderleftcolor="#36f" o:borderbottomcolor="#36f" o:borderrightcolor="#36f"> <v:imagedata src="/help/imgFrHelp/image235.png" o:title=""/> <w:bordertop type="single" width="12"/> <w:borderleft type="single" width="12"/> <w:borderbottom type="single" width="12"/> <w:borderright type="single" width="12"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image236.jpg" v:shapes="_x0000_i1161" border="0" height="214" width="422"><!--[endif]--></p> <p class="MsoNormal" style="text-indent: 0.65pt; page-break-after: avoid;"><!--[if gte vml 1]><v:shape id="_x0000_i1162" type="#_x0000_t75" style='width:340.5pt;height:297.75pt' o:ole=""> <v:imagedata src="/help/imgFrHelp/image237.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image238.jpg" v:shapes="_x0000_i1162" border="0" height="397" width="454"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1162" DrawAspect="Content" ObjectID="_1473694211"> </o:OLEObject> </xml><![endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193856">Figure </a><!--[if supportFields]><span style='mso-bookmark:_Toc364193856'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193856'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><![endif]--><span style=""><span style="">99</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193856'></span><span style='mso-element:field-end'></span><![endif]--><span style=""> : insertion d'images et animation</span></p> </td> </tr> </tbody> </table> </div> </div> <br> <!-- Begin of UNDER_BOXES --> <div id="UnderBoxes"> </div> <!-- End of UNDER_BOXES --> </td> </tr> </tbody> </table> </body></html>