{"id":4677,"date":"2012-06-21T17:11:35","date_gmt":"2012-06-21T21:11:35","guid":{"rendered":"http:\/\/cscircles.cemc.uwaterloo.ca\/?page_id=4677"},"modified":"2013-08-07T19:47:55","modified_gmt":"2013-08-07T23:47:55","slug":"11c-fr","status":"publish","type":"page","link":"https:\/\/cscircles.cemc.uwaterloo.ca\/dev\/11c-fr\/","title":{"rendered":"11C: G\u00e9om\u00e9trie"},"content":{"rendered":"<!-- Please retain this notice and add more notes if you create a new version.<br \/>\nMain French translator: Brice Canvel, brice.canvel@gmail.com<br \/>\nOriginal lesson author: David Pritchard, daveagp@gmail.com<br \/>\nLicense: http:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/<br \/>\nFor the full site, visit http:\/\/cscircles.ca-->\n<p><em>La le\u00e7on 11 est compos\u00e9e de trois partie A, B et C qui peuvent \u00eatre compl\u00e9t\u00e9es dans n'importe quel ordre.<\/em><\/p>\n<p>Dans cet exercice, nous allons cr\u00e9er quatre fonctions qui calculent des mesures g\u00e9om\u00e9triques:<\/p>\n<ul>\n<li>une fonction qui calcule la longueur de l'hypot\u00e9nuse d'un triangle rectangle,<\/li>\n<li>une fonction qui calcule le p\u00e9rim\u00e8tre d'un triangle rectangle,<\/li>\n<li>une fonction qui calcule le distance entre deux points dans le plan,<\/li>\n<li>et une fonction qui calcule le p\u00e9rim\u00e8tre d'un triangle quelconque.<\/li>\n<\/ul>\n<h2>Hypot\u00e9nuse<\/h2>\n<p><img decoding=\"async\" class=\"alignright  wp-image-1606\" style=\"margin-top: -2em;\" title=\"hypotenuse\" src=\"..\/wp-content\/lesson_files\/img\/11C\/hypotenuse-fr.png\" alt=\"\" \/>Vous pouvez voir un <em>triangle rectangle<\/em> sur la figure \u00e0 droite. Par d\u00e9finition, un des angles d'un triangle rectangle mesure 90 degr\u00e9s (un <em>angle droit<\/em>). Le triangle a trois c\u00f4t\u00e9s. Le c\u00f4t\u00e9 oppos\u00e9 \u00e0 l'angle droit porte le nom d'<em>hypot\u00e9nuse.<\/em><\/p>\n<p>Comme indiqu\u00e9 sur le diagramme, <em>a<\/em> et <em>b<\/em> repr\u00e9sentent la longueur des c\u00f4t\u00e9s adjancents \u00e0 l'angle droit et <em>c<\/em> la longueur de l'hypot\u00e9nuse. La fameux th\u00e9or\u00e8me de Pythagore nous dit que<\/p>\n<p style=\"text-align: center;\"><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle%7Ba%5E2%2Bb%5E2%3Dc%5E2%7D&#038;bg=T&#038;fg=000000&#038;s=2' alt='\\displaystyle{a^2+b^2=c^2}' title='\\displaystyle{a^2+b^2=c^2}' class='latex' \/><\/p>\n<p>Dans le premier probl\u00e8me, votre t\u00e2che est de convertir ce probl\u00e8me en une fonction qui, \u00e9tant donn\u00e9 <em>a<\/em> et <em>b<\/em>, calcule la longueur de l'hypot\u00e9nuse.<\/p>\n<p><form class=\"pbform\" action=\"#\" id=\"pbform0\" method=\"POST\">\n<div class='pybox modeNeutral ' id='pybox0'>\n<img title='You have not yet completed this problem.' src='https:\/\/cscircles.cemc.uwaterloo.ca\/dev\/wp-content\/plugins\/pybox\/files\/icon.png' class='pycheck'\/><div class=\"heading\"><span class='type'>Coding Exercise: <\/span><span class='title'>Hypot\u00e9nuse<\/span><\/div>D\u00e9finissez une foncion\u00a0<code>hypotenuse(a, b)<\/code> \u200eretourne la longueur de l'hypot\u00e9nuse\u00a0<em>c<\/em>, si les deux autres c\u00f4t\u00e9s ont pour longueurs <em>a<\/em> et <em>b<\/em>.\u00a0<a class=\"hintlink\"  id=\"hintlink1\">Hint<\/a><div class=\"helpOuter\" style=\"display: none;\"><div class=\"helpInner\"><div style=\"text-align: center\">You need to create an account and log in to ask a question.<\/div><\/div><\/div><div class='pyboxTextwrap pyboxCodewrap RW resizy'  style='height: 526px;'><textarea wrap='off' name='usercode0' id='usercode0'  cols=10 rows=20   class='pyboxCode RW'>\n# delete this comment and enter your code here\n<\/textarea><\/div>\n<div id='pbhistory0' class='flexcontain' style='display:none;'><\/div>\n<div name=\"pyinput\" id=\"pyinput0\">Enter testing statements like <code>print(myfunction(\"test argument\"))<\/code> below.<div class=\"pyboxTextwrap resizy\" style=\"height: 102px;\" ><textarea wrap=\"off\" name=\"userinput\" class=\"pyboxInput\" cols=10 rows=4><\/textarea><\/div><\/div>\n<div class='pyboxbuttons'><table><tr>\n<td><input type='submit' name='submit' id='submit0' value=' '\/><\/td>\n<td><input type='button' name='switch' id=\"switch0\" value=\"Input Switch\" onclick=\"pbInputSwitch(0,'Y')\" ><\/td>\n<td><input type='button' name='consolecopy' value=\"Open in console\" onclick=\"pbConsoleCopy(0)\" ><\/td>\n<td><input type='button' name='visualize' value=\"Visualize\" onclick=\"pbVisualize(0,'Y')\" ><\/td>\n<\/tr><\/table><select id='pbSelect0' class='selectmore'><option name='more'>More actions...<\/option>\n<option name='history' data-pbonclick=\"historyClick(0,'11c.hypotenuse')\" >History<\/option>\n<option name='help' data-pbonclick=\"helpClick(0);\" >Help<\/option>\n<\/select><\/div>\n<input type=\"hidden\" name=\"lang\" value=\"\"\/><input type=\"hidden\" id=\"inputInUse0\" name=\"inputInUse\" value=\"Y\"\/>\n<input type=\"hidden\" name=\"pyId\" value=\"0\"\/>\n<input type=\"hidden\" name=\"hash\" value=\"6bb2053bf0c646f94ad6080b220c2890\"\/>\n<div id='pbresults0' class='pbresults avoidline'><\/div>\n<\/div>\n<\/form>\n<script type='text\/javascript'>jQuery(function(){pbToggleCodeMirror(0);});pbInputSwitch(0,\"Y\");<\/script>\n<\/p>\n<h2>P\u00e9rim\u00e8tre<\/h2>\n<p>Souvenez-vous que le <em>p\u00e9rim\u00e8tre<\/em> d'un triangle est la somme de ses c\u00f4t\u00e9s. Donc, sur le diagramme ci-dessus, le p\u00e9rim\u00e8tre est la longueur <em>a+b+c<\/em>.\u00a0<strong>Votre programme assumera <\/strong> qu'une version de la fonction\u00a0<code>hypotenuse<\/code> a d\u00e9j\u00e0 \u00e9t\u00e9 d\u00e9finie (vous n'avez pas besoin de copier votre code de l'exercice pr\u00e9cedent).<\/p>\n<p><form class=\"pbform\" action=\"#\" id=\"pbform2\" method=\"POST\">\n<div class='pybox modeNeutral ' id='pybox2'>\n<img title='You have not yet completed this problem.' src='https:\/\/cscircles.cemc.uwaterloo.ca\/dev\/wp-content\/plugins\/pybox\/files\/icon.png' class='pycheck'\/><div class=\"heading\"><span class='type'>Coding Exercise: <\/span><span class='title'>Les droits des triangles<\/span><\/div>En utilisant <code>hypotenuse(a, b)<\/code>, d\u00e9finissez une fonction\u00a0<code>perimetreTriangleRectangle(a, b)<\/code> qui retourne la longueur du p\u00e9rim\u00e8tre d'un triangle rectangle dont les deux c\u00f4t\u00e9s adjacents \u00e0 l'angle droit ont pour longueurs\u00a0<em>a<\/em> et\u00a0<em>b<\/em>.<div class=\"helpOuter\" style=\"display: none;\"><div class=\"helpInner\"><div style=\"text-align: center\">You need to create an account and log in to ask a question.<\/div><\/div><\/div><div class='pyboxTextwrap pyboxCodewrap RW resizy'  style='height: 526px;'><textarea wrap='off' name='usercode2' id='usercode2'  cols=10 rows=20   class='pyboxCode RW'>\n# delete this comment and enter your code here\n<\/textarea><\/div>\n<div id='pbhistory2' class='flexcontain' style='display:none;'><\/div>\n<div name=\"pyinput\" id=\"pyinput2\">Enter testing statements like <code>print(myfunction(\"test argument\"))<\/code> below.<div class=\"pyboxTextwrap resizy\" style=\"height: 102px;\" ><textarea wrap=\"off\" name=\"userinput\" class=\"pyboxInput\" cols=10 rows=4><\/textarea><\/div><\/div>\n<div class='pyboxbuttons'><table><tr>\n<td><input type='submit' name='submit' id='submit2' value=' '\/><\/td>\n<td><input type='button' name='switch' id=\"switch2\" value=\"Input Switch\" onclick=\"pbInputSwitch(2,'Y')\" ><\/td>\n<td><input type='button' name='consolecopy' value=\"Open in console\" onclick=\"pbConsoleCopy(2)\" ><\/td>\n<td><input type='button' name='visualize' value=\"Visualize\" onclick=\"pbVisualize(2,'Y')\" ><\/td>\n<\/tr><\/table><select id='pbSelect2' class='selectmore'><option name='more'>More actions...<\/option>\n<option name='history' data-pbonclick=\"historyClick(2,'11c.rightperimeter')\" >History<\/option>\n<option name='help' data-pbonclick=\"helpClick(2);\" >Help<\/option>\n<\/select><\/div>\n<input type=\"hidden\" name=\"lang\" value=\"\"\/><input type=\"hidden\" id=\"inputInUse2\" name=\"inputInUse\" value=\"Y\"\/>\n<input type=\"hidden\" name=\"pyId\" value=\"2\"\/>\n<input type=\"hidden\" name=\"hash\" value=\"a83e931746113bc911eeb8903577da9f\"\/>\n<div id='pbresults2' class='pbresults avoidline'><\/div>\n<\/div>\n<\/form>\n<script type='text\/javascript'>jQuery(function(){pbToggleCodeMirror(2);});pbInputSwitch(2,\"Y\");<\/script>\n<\/p>\n<h2>Distance en 2 Dimensions<\/h2>\n<p>Pour parler de deux points en deux dimensions, nous les sp\u00e9cifions en utilisant deux coordonn\u00e9es (<a href=\"http:\/\/fr.wikipedia.org\/wiki\/Coordonn%C3%A9es_cart%C3%A9siennes\" target=\"_blank\">syst\u00e8me de cooordonn\u00e9es Cart\u00e9sien<\/a>), la coordonn\u00e9e <em>x<\/em> et la coordonn\u00e9e <em>y<\/em>. Nous voulons \u00e9crire une fonction dont l'entr\u00e9e est une paire de points et la sortie est la distance entre ces deux points. Il s'av\u00e8re que la fonction <code>hypotenuse<\/code> peut nous aider \u00e0 accomplir cette t\u00e2che !<\/p>\n<p>Soient le premier point de coordonn\u00e9es (x1, y1) o\u00f9 x1 et y1 sont des nombres r\u00e9els, et le deuxi\u00e8me point de coordonn\u00e9es (x2, y2). L'id\u00e9e est de dessiner le triangle rectangle que vous voyez sur le diagramme ci-dessous: l'hypot\u00e9nuse va de (x1, x2) \u00e0 (y1, y2) et donc sa longueur est \u00e9gale \u00e0 la distance entre ces deux points.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"aligncenter\" src=\"..\/wp-content\/lesson_files\/img\/11C\/distance2d-fr.png\" alt=\"\" \/><\/p>\n<p>Pour calculer la longueur de l'hypot\u00e9nuse,\u00a0nous devons calculer la longueur des deux autres c\u00f4t\u00e9s du triangle. Cela se fait en utilisant la d\u00e9finition des coordonn\u00e9es (voir diagramme): le d\u00e9placement horizontal est\u00a0<em>a<\/em> = x1-x2 et le d\u00e9placement vertical est\u00a0<em>b<\/em> = y1-y2.<\/p>\n<p><form class=\"pbform\" action=\"#\" id=\"pbform3\" method=\"POST\">\n<div class='pybox modeNeutral ' id='pybox3'>\n<img title='You have not yet completed this problem.' src='https:\/\/cscircles.cemc.uwaterloo.ca\/dev\/wp-content\/plugins\/pybox\/files\/icon.png' class='pycheck'\/><div class=\"heading\"><span class='type'>Coding Exercise: <\/span><span class='title'>Distance 2D<\/span><\/div>Assumez que la fonction\u00a0<code>hypotenuse(a, b)<\/code> a d\u00e9j\u00e0 \u00e9t\u00e9 d\u00e9finie. En vous aidant de cette fonction, d\u00e9finissez une fonction\u00a0<code>distance2D(x1, y1, x2, y2)<\/code> qui calcule la distance entre le point (x1, y1) et le point (x2, y2).<div class=\"helpOuter\" style=\"display: none;\"><div class=\"helpInner\"><div style=\"text-align: center\">You need to create an account and log in to ask a question.<\/div><\/div><\/div><div class='pyboxTextwrap pyboxCodewrap RW resizy'  style='height: 526px;'><textarea wrap='off' name='usercode3' id='usercode3'  cols=10 rows=20   class='pyboxCode RW'>\n# delete this comment and enter your code here\n<\/textarea><\/div>\n<div id='pbhistory3' class='flexcontain' style='display:none;'><\/div>\n<div name=\"pyinput\" id=\"pyinput3\">Enter testing statements like <code>print(myfunction(\"test argument\"))<\/code> below.<div class=\"pyboxTextwrap resizy\" style=\"height: 102px;\" ><textarea wrap=\"off\" name=\"userinput\" class=\"pyboxInput\" cols=10 rows=4><\/textarea><\/div><\/div>\n<div class='pyboxbuttons'><table><tr>\n<td><input type='submit' name='submit' id='submit3' value=' '\/><\/td>\n<td><input type='button' name='switch' id=\"switch3\" value=\"Input Switch\" onclick=\"pbInputSwitch(3,'Y')\" ><\/td>\n<td><input type='button' name='consolecopy' value=\"Open in console\" onclick=\"pbConsoleCopy(3)\" ><\/td>\n<td><input type='button' name='visualize' value=\"Visualize\" onclick=\"pbVisualize(3,'Y')\" ><\/td>\n<\/tr><\/table><select id='pbSelect3' class='selectmore'><option name='more'>More actions...<\/option>\n<option name='history' data-pbonclick=\"historyClick(3,'11c.distance')\" >History<\/option>\n<option name='help' data-pbonclick=\"helpClick(3);\" >Help<\/option>\n<\/select><\/div>\n<input type=\"hidden\" name=\"lang\" value=\"\"\/><input type=\"hidden\" id=\"inputInUse3\" name=\"inputInUse\" value=\"Y\"\/>\n<input type=\"hidden\" name=\"pyId\" value=\"3\"\/>\n<input type=\"hidden\" name=\"hash\" value=\"76df98374fdf721ce9a961094d5b016a\"\/>\n<div id='pbresults3' class='pbresults avoidline'><\/div>\n<\/div>\n<\/form>\n<script type='text\/javascript'>jQuery(function(){pbToggleCodeMirror(3);});pbInputSwitch(3,\"Y\");<\/script>\n<\/p>\n<h2>P\u00e9rim\u00e8tre de n'importe quel triangle<\/h2>\n<p>Nous voici arriv\u00e9 au dernier exercice de cette le\u00e7on. Souvenez-vous que le p\u00e9rim\u00e8tre est la somme des longueurs des c\u00f4t\u00e9s du triangle et notez que la longueur est en fait la distance entre deux points du triangle.<\/p>\n<p><form class=\"pbform\" action=\"#\" id=\"pbform4\" method=\"POST\">\n<div class='pybox modeNeutral ' id='pybox4'>\n<img title='You have not yet completed this problem.' src='https:\/\/cscircles.cemc.uwaterloo.ca\/dev\/wp-content\/plugins\/pybox\/files\/icon.png' class='pycheck'\/><div class=\"heading\"><span class='type'>Coding Exercise: <\/span><span class='title'>S\u00e9curisez le P\u00e9rim\u00e8tre<\/span><\/div>Supposez que la fonction <code>distance2D(x1, y1, x2, y2)<\/code> est d\u00e9j\u00e0 d\u00e9finie. En utilisant cette fonction, d\u00e9finissez une fonction\u00a0<code>trianglePerimeter(xA, yA, xB, yB, xC, yC)<\/code> qui calcule le p\u00e9rim\u00e8tre d'un triangle dont les sommets sont les points (xA, yA), (xB, yB) et (xC, yC).<div class=\"helpOuter\" style=\"display: none;\"><div class=\"helpInner\"><div style=\"text-align: center\">You need to create an account and log in to ask a question.<\/div><\/div><\/div><div class='pyboxTextwrap pyboxCodewrap RW resizy'  style='height: 526px;'><textarea wrap='off' name='usercode4' id='usercode4'  cols=10 rows=20   class='pyboxCode RW'>\n# delete this comment and enter your code here\n<\/textarea><\/div>\n<div id='pbhistory4' class='flexcontain' style='display:none;'><\/div>\n<div name=\"pyinput\" id=\"pyinput4\">Enter testing statements like <code>print(myfunction(\"test argument\"))<\/code> below.<div class=\"pyboxTextwrap resizy\" style=\"height: 102px;\" ><textarea wrap=\"off\" name=\"userinput\" class=\"pyboxInput\" cols=10 rows=4><\/textarea><\/div><\/div>\n<div class='pyboxbuttons'><table><tr>\n<td><input type='submit' name='submit' id='submit4' value=' '\/><\/td>\n<td><input type='button' name='switch' id=\"switch4\" value=\"Input Switch\" onclick=\"pbInputSwitch(4,'Y')\" ><\/td>\n<td><input type='button' name='consolecopy' value=\"Open in console\" onclick=\"pbConsoleCopy(4)\" ><\/td>\n<td><input type='button' name='visualize' value=\"Visualize\" onclick=\"pbVisualize(4,'Y')\" ><\/td>\n<\/tr><\/table><select id='pbSelect4' class='selectmore'><option name='more'>More actions...<\/option>\n<option name='history' data-pbonclick=\"historyClick(4,'11c.perimeter')\" >History<\/option>\n<option name='help' data-pbonclick=\"helpClick(4);\" >Help<\/option>\n<\/select><\/div>\n<input type=\"hidden\" name=\"lang\" value=\"\"\/><input type=\"hidden\" id=\"inputInUse4\" name=\"inputInUse\" value=\"Y\"\/>\n<input type=\"hidden\" name=\"pyId\" value=\"4\"\/>\n<input type=\"hidden\" name=\"hash\" value=\"15cb528f09907c81cb91e63e3e01e00d\"\/>\n<div id='pbresults4' class='pbresults avoidline'><\/div>\n<\/div>\n<\/form>\n<script type='text\/javascript'>jQuery(function(){pbToggleCodeMirror(4);});pbInputSwitch(4,\"Y\");<\/script>\n<\/p>\n<p>Vous \u00eates pr\u00eats pour la prochaine le\u00e7on!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>La le\u00e7on 11 est compos\u00e9e de trois partie A, B et C qui peuvent \u00eatre compl\u00e9t\u00e9es dans n'importe quel ordre. Dans cet exercice, nous allons cr\u00e9er quatre fonctions qui calculent des mesures g\u00e9om\u00e9triques: une fonction qui calcule la longueur de &hellip; <a href=\"https:\/\/cscircles.cemc.uwaterloo.ca\/dev\/11c-fr\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-4677","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/cscircles.cemc.uwaterloo.ca\/dev\/wp-json\/wp\/v2\/pages\/4677","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cscircles.cemc.uwaterloo.ca\/dev\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/cscircles.cemc.uwaterloo.ca\/dev\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/cscircles.cemc.uwaterloo.ca\/dev\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cscircles.cemc.uwaterloo.ca\/dev\/wp-json\/wp\/v2\/comments?post=4677"}],"version-history":[{"count":19,"href":"https:\/\/cscircles.cemc.uwaterloo.ca\/dev\/wp-json\/wp\/v2\/pages\/4677\/revisions"}],"predecessor-version":[{"id":7472,"href":"https:\/\/cscircles.cemc.uwaterloo.ca\/dev\/wp-json\/wp\/v2\/pages\/4677\/revisions\/7472"}],"wp:attachment":[{"href":"https:\/\/cscircles.cemc.uwaterloo.ca\/dev\/wp-json\/wp\/v2\/media?parent=4677"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}