<HTML> <HEAD>   <meta name="Author" content="ketRoux"> <meta http-equiv="content-language" content="fr"> <meta name="revisit-after" content="7 days"> <META NAME="Description" content="Cylindre coup par un plan."> <META NAME="Keywords" content="math,mathmatiques,cylindre,intersection,patron d'un cylindre"> <META NAME="Creation_Date" content="15/12/99">     <TITLE>Cylindre coup&eacute; par un plan.</TITLE>    <X-SAS-WINDOW TOP=0 BOTTOM=489 LEFT=0 RIGHT=796> </HEAD> <BODY BGCOLOR="#FFFFEC" LINK="#FF1319" VLINK="#FF1414" background="fond.gif">  <P><CENTER><A NAME="Depart"></A><TABLE BORDER=1>    <TR>       <TD WIDTH=410 HEIGHT=81>          <P><CENTER><FONT SIZE="+2" COLOR="#0000AF">Cylindre de          r&eacute;volution coup&eacute; par un plan. (style tour de          Pise.)</FONT></CENTER>       </TD></TR> </TABLE></CENTER></P>  <P><FONT SIZE="+1" COLOR="#0000AF">&nbsp;</FONT></P>  <P><FONT SIZE="+1" COLOR="#0000AF">&nbsp;</FONT></P>  <P><CENTER><U><FONT SIZE="+1" COLOR="#0000AF">Probl&egrave;me </FONT></U><FONT SIZE="+1" COLOR="#0000AF">: Quel est le patron d'un cylindre de r&eacute;volution coup&eacute; par un plan ?</FONT> </CENTER></P>  <P><FONT SIZE="+1" COLOR="#0000AF">&nbsp;</FONT></P>  <P><FONT SIZE="+1" COLOR="#0000AF">NON, ce n'est pas en g&eacute;n&eacute;ral un parall&eacute;logramme. Pour vous en convaincre il suffit d'ouvrir le carton d'un rouleau de papier "</FONT><I><FONT SIZE="+1" COLOR="#0000AF"> Essuie&nbsp;tout </FONT></I><FONT SIZE="+1" COLOR="#0000AF">" par exemple.</FONT></P>  <P><CENTER><FONT SIZE="+1" COLOR="#0000AF">&nbsp;</FONT> </CENTER></P>  <P><CENTER><FONT SIZE="+1" COLOR="#0000AF"><A HREF="#Debut">Suite</A></FONT><FONT SIZE="+1" COLOR="#0000AF"> </FONT><FONT SIZE="+1" COLOR="#0000AF"><A HREF="../index.html">Accueil</A></FONT> </CENTER></P>  <P><CENTER><FONT SIZE="+1" COLOR="#0000AF">&nbsp;</FONT> </CENTER></P>  <P><CENTER><FONT SIZE="+1" COLOR="#0000AF">&nbsp;</FONT> </CENTER></P>  <P><CENTER><FONT SIZE="+1" COLOR="#0000AF">&nbsp;</FONT> </CENTER></P>  <P><CENTER><FONT SIZE="+1" COLOR="#0000AF"><A NAME="Debut"></A></FONT><TABLE BORDER=1>    <TR>       <TD WIDTH="374">          <P><FONT SIZE="+1" COLOR="#0000AF">&nbsp;</FONT></P>                    <P><FONT SIZE="+1" COLOR="#0000AF">On a un cylindre de          r&eacute;volution coup&eacute; par des plans          parall&egrave;les au plan noir d'&eacute;quation :</FONT>          </P>                    <P><CENTER><FONT SIZE="+1" COLOR="#0000AF">z = y. tan          (a)</FONT></CENTER></P>                    <P><FONT SIZE="+1" COLOR="#0000AF">o&ugrave; a est l'angle          des deux plans rouge et noir.</FONT></P>                    <P><CENTER><FONT COLOR="#0000AF">(ici tan (a) = 0,5.)</FONT>          </CENTER></P>                    <P>&nbsp;</P>                    <P>&nbsp;</P>                                        <P><CENTER><FONT SIZE="+1"          COLOR="#0000AF"><A HREF="#Fin">Suite</A></FONT><FONT          SIZE="+1" COLOR="#0000AF"> </FONT><FONT SIZE="+1"          COLOR="#0000AF"><A HREF="../index.html">Retour</A></FONT>          </CENTER>       </TD><TD WIDTH="380">          <P><CENTER><IMG          SRC="cyl_g.gif"          WIDTH=294 HEIGHT=471 ALIGN=middle></CENTER>       </TD></TR> </TABLE></CENTER></P>  <P><CENTER><FONT SIZE="+1" COLOR="#0000AF">&nbsp;</FONT> </CENTER></P>  <P><FONT SIZE="+1" COLOR="#0000AF">&nbsp;</FONT></P>  <P><FONT SIZE="+1" COLOR="#0000AF">&nbsp;</FONT></P>  <P><FONT SIZE="+1" COLOR="#0000AF">&nbsp;</FONT></P>  <P><FONT SIZE="+1" COLOR="#0000AF"><A NAME="Fin"></A></FONT></P>  <P><CENTER><TABLE BORDER=1>    <TR>       <TD WIDTH="380">          <P><FONT SIZE="+1" COLOR="#0000AF">Soit M( x ; y ; 0          )&nbsp;</FONT></P>                    <P><FONT COLOR="#0000AF">&nbsp;</FONT><FONT SIZE="+1"          COLOR="#0000AF">En mesure alg&eacute;brique Mm = y.tan(          a)</FONT></P>                    <P><FONT SIZE="+1" COLOR="#0000AF">Soit x la longueur de          l'arc AM .</FONT></P>                    <P><FONT SIZE="+1" COLOR="#0000AF">x = Rt avec t dans [0 ; 2          </FONT><FONT SIZE="+1" FACE="Symbol" COLOR="#0000AF">p          ]</FONT><FONT SIZE="+1" COLOR="#0000AF">.</FONT></P>                    <P><FONT SIZE="+1" COLOR="#0000AF">Or y = R cos t </FONT>          </P>                    <P><FONT SIZE="+1" COLOR="#0000AF">D'o&ugrave; : </FONT>          </P>                    <P><FONT SIZE="+1" COLOR="#0000AF">f(x) =R.tan( a).cos(x/R)          avec x dans [0 ; 2</FONT><FONT SIZE="+1" FACE="Symbol"          COLOR="#0000AF">p</FONT><FONT SIZE="+1" COLOR="#0000AF">          .R]</FONT><FONT SIZE="+1" COLOR="#0000AF">.</FONT></P>                    <P><FONT SIZE="+1" COLOR="#0000AF">&nbsp;</FONT></P>                    <P><FONT SIZE="+1" COLOR="#0000AF">Le bord du patron est          donc une sinuso&iuml;de</FONT><FONT SIZE="+1"          COLOR="#0000AF">.</FONT></P>                    <P><CENTER><FONT SIZE="+1"          COLOR="#0000AF"><A HREF="#Courbe">Suite</A></FONT><FONT          SIZE="+1" COLOR="#0000AF"> </FONT><FONT SIZE="+1"          COLOR="#0000AF"><A HREF="../index.html">Retour</A></FONT>          </CENTER>       </TD><TD WIDTH="378">          <P><CENTER><FONT SIZE="+1" COLOR="#0000AF"><IMG          SRC="cyl_g.gif"          WIDTH=294 HEIGHT=471 ALIGN=middle></FONT></CENTER>       </TD></TR> </TABLE></CENTER></P>  <P>&nbsp;</P>  <P>&nbsp;</P>  <P>&nbsp;</P>  <P>&nbsp;</P>  <P>&nbsp;</P>  <P><CENTER>&nbsp;<A NAME="Courbe"></A><FONT COLOR="#0000AF">&nbsp;</FONT><FONT SIZE="+1" COLOR="#0000AF">Voici le patron.&nbsp;&nbsp;&nbsp;&nbsp;</FONT><FONT COLOR="#0000AF"> </FONT><FONT SIZE="+1" COLOR="#0000AF"><A HREF="#Depart">D&eacute;but</A></FONT><FONT SIZE="+1" COLOR="#0000AF"> &nbsp;&nbsp;&nbsp;</FONT><FONT SIZE="+1" COLOR="#0000AF"><A HREF="../index.html">Retour</A></FONT> </CENTER></P>  <P><CENTER><FONT COLOR="#0000AF"><IMG SRC="Patrcyl.gif" WIDTH=717 HEIGHT=425 ALIGN=bottom></FONT></CENTER></P> </BODY> </HTML> <!-- DEBUT / Cybermonitor / START --> <script language="javascript"><!-- CM_RUBRIQUE = "edit_PagesPersos_abonnes"; 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