{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot " 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1533 "restart:with(plots ):with(plottools):\na:=1:b:=0.95:\nr1:=piecewise(b**4-a**4*sin(2*t)**2 >=0,sqrt(a**2*cos(2*t)+Re(sqrt(b**4-a**4*sin(2*t)**2))),FAIL):r2:=piec ewise(b**4-a**4*sin(2*t)**2>=0,sqrt(a**2*cos(2*t)-Re(sqrt(b**4-a**4*si n(2*t)**2))),FAIL): #construction des arcs de courbe\ng:=polarplot([r 1,r2],t=-Pi/2..Pi/2,scaling=constrained,color=red,numpoints=200):\n # r\351cup\351ration des points du premier arc\ns1:=op(1,op(g)[1]):\n # r\351cup\351ration des points du second arc et inversion de l'ordre de s points\ns2:=op(1,op(g)[2]):n:=nops(s2):s2:=[seq(s2[n-k],k=0..n-1)]: \n #suppression des coordonn\351es en \351chec\np:=subs([undefined$2] =NULL,[op(s1),op(s2)]):\n #bouclage de la ligne polygonale sur son pr emier point\np:=[op(p),p[1]]:\nh:=plot([p,map(x->-x,p)],color=red,scal ing=constrained,thickness=2):\npuiss:=sqrt(1-b^4):\nu:=sqrt(0.5+puiss/ 2):\nv:=sqrt(0.5-puiss/2):\ntheta:=arctan(v^4/u^4):\nr:=u*v/sqrt(v^2*c os(t)^2-u^2*sin(t)^2):\nfigure1:=polarplot(r,t=0..2*Pi,color=blue,nump oints=300) #l'hyperbole\n,plot([v/u*x,-v/u*x],x=-3..3,colo r=blue,linestyle=8) #ses asymptotes\n,circle([0,0],sqrt(abs(puiss)),co lor=green, thickness=1) # cercle d'inversion\n,h: \+ #enfin l'oval e\nfigure:=NULL:\nn:=20:\nfor k from 0 to n do\nt:=-theta+2*k*theta/n: \nfigure:=figure,display(circle(evalf([r*cos(t),r*sin(t)]),sqrt(r^2-pu iss)),color=black):\nod:\nfor k from 0 to n do\nt:=-theta+2*k*theta/n: \nfigure:=figure,display(circle(evalf([-r*cos(t),r*sin(t)]),sqrt(r^2-p uiss)),color=black):\nod:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "display([figure1,display(figure,insequence=false)],scaling=constr ained,thickness=0,view=[-2..2,-2..2],axes=none);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 49 }{VIEWOPTS 1 1 0 1 1 1803 }