{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "moi" -1 256 "Times" 1 12 0 0 1 1 0 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 1 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 3 0 3 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 0 " -1 256 1 {CSTYLE "" -1 -1 "Monaco" 1 9 0 0 255 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE " " -1 -1 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "interface(plotdevice =ps,plotoutput=`C:/courbes/anticaustique.eps`,plotoptions=`portrait,no border`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 183 "with(plots):w ith(plottools):\narc:=proc(A,B,C,r) local a,b:\na:=arctan(A[2]-B[2],A[ 1]-B[1]):\nb:=arctan(C[2]-B[2],C[1]-B[1]):\nplot([B[1]+r*cos(t),B[2]+r *sin(t),t=a..b],color=black);\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "x:=t->t: y:=t->2+t*(1-t):\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "#equations param\351triques de la tangente\nxt:= t->x(u)+D(x)(u)*t;yt:=t->y(u)+D(y)(u)*t;" }}{PARA 11 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%#xtGf*6#%\"tG6\"6$%)operatorG%&arrowGF(,&-%\"xG6#%\"uG\"\"\"*&--%\" DG6#F.F/F19$F1F1F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ytGf*6#% \"tG6\"6$%)operatorG%&arrowGF(,&-%\"yG6#%\"uG\"\"\"*&--%\"DG6#F.F/F19$ F1F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 204 "#intersectio n de la tangente et du rayon vecteur\nu:=0.25:\ntT:=solve(yt(t)/xt(t)= -x(u)/y(u),t):\nT:=[xt(tT),yt(tT)]:R0:=sqrt(x(u)**2+y(u)**2):\nR:=sqrt (((x(u)+xt(tT))/2)**2+((y(u)+yt(tT))/2)**2):\nr0:=R0*0.5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 316 "a:=-5:b:=4:c:=-1:d:=5:\nplot([[x(u )+cos(t)*r0,y(u)+sin(t)*r0,t=0..2*Pi],[x(u)+cos(t)*R0,y(u)+sin(t)*R0,t =0..2*Pi],[(x(u)+xt(tT))/2+R*cos(t),(y(u)+yt(tT))/2+R*sin(t),t=0..2*Pi ],[x(t),y(t),t=-0.5..2],[T,[0,0],[x(u),y(u)]],[[xt(-5),yt(-5)],[xt(2.5 ),yt(2.5)]]],color=black,view=[a..b,c..d],axes=none,scaling=constraine d);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "#Calcul des points N+ et N-\nsolve(\{(xx-x(u))**2+(y y-y(u))**2=r0**2,(xx-(x(u)+xt(tT))/2)**2+(yy-(y(u)+yt(tT))/2)**2=R**2 \},\{xx,yy\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<$/%#xxG$\"+)Q3)[X!# 5/%#yyG$\"+@L'e5\"!\"*<$/F%$!+(R3Q#\\F(/F*$\"+ymQ+IF-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "T:=[x-(x^2+y^2)*x1/(xx1+yy1),y-(x^2 +y^2)*y1/(xx1+yy1)];M:=[x,y];U:=expand((M+T)/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"TG7$,&%\"xG\"\"\"*(,&*$)F'\"\"#F(F(*$)%\"yGF-F(F(F( %#x1GF(,&%$xx1GF(%$yy1GF(!\"\"F5,&F0F(*(F*F(%#y1GF(F2F5F5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG7$%\"xG%\"yG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UG7$,(%\"xG\"\"\"**\"\"#!\"\"%#x1GF(,&%$xx1GF(%$yy1 GF(F+F'F*F+**F*F+F,F(F-F+%\"yGF*F+,(F1F(**F*F+%#y1GF(F-F+F'F*F+**F*F+F 4F(F-F+F1F*F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "eq1:=(X-x) ^2+(Y-y)^2-(x^2+y^2)/n;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G,(*$ ),&%\"XG\"\"\"%\"xG!\"\"\"\"#F*F**$),&%\"YGF*%\"yGF,F-F*F**&,&*$)F+F-F *F**$)F2F-F*F*F*%\"nGF,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "eq2:=(X-U[1])^2+(Y-U[2])^2-((M[1]-T[1])^2+(M[2]-T[2])^2)/4;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G,**$),*%\"XG\"\"\"%\"xG!\"\"** \"\"#F,%#x1GF*,&%$xx1GF*%$yy1GF*F,F+F.F***F.F,F/F*F0F,%\"yGF.F*F.F*F** $),*%\"YGF*F4F,**F.F,%#y1GF*F0F,F+F.F***F.F,F:F*F0F,F4F.F*F.F*F***\"\" %F,,&*$)F+F.F*F**$)F4F.F*F*F.F/F.F0!\"#F,**F=F,F>F.F:F.F0FCF," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "solve(\{eq1,eq2\},\{X,Y\}); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<$/%\"YG*&-%'RootOfG6$,8*()%#x1G\" \"#\"\"\"%\"nGF/)%\"xGF.F/!\"\"*,F.F/%$xx1GF/F0F/%\"yGF/%#y1GF/F3*(F,F /F0F/)F6F.F/F3*(F.F/F5F/%$yy1GF/F/*$)F;F.F/F/*,F.F/F;F/F0F/F6F/F7F/F3* ()F0F.F/F,F/F9F/F/*$)F5F.F/F/*(F@F/F9F/)F7F.F/F/*&,***F.F/F0F/FDF/F6F/ F3**F.F/F0F/F6F/F,F/F3*(F.F/F7F/F5F/F/*(F.F/F7F/F;F/F/F/%#_ZGF/F/*&,&* $F,F/F/*$FDF/F/F/)FKF.F/F//%&labelG%$_L1GF/F0F3/%\"XG*(,,*&F7F/F'F/F3* (F0F/F-F/F2F/F/F5F3F;F3*(F0F/F6F/F7F/F/F/F0F3F-F3" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "11 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }