{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{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 "Headi ng 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 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 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 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 "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" {TEXT -1 50 "War ning, the name changecoords has been redefined\n" }}}{EXCHG {PARA 18 " " 0 "" {TEXT -1 14 "Ellipsographes" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 39 " Ellipsographe par anti-parall\351logramme" }}{EXCHG {PARA 0 " " 0 "" {TEXT -1 151 "Tiges articul\351es AB, BC, CD formant un quadril at\350re non convexe : A et D fixes, AB=CD, AD=BC ; le point d'interse ction E de AB et CD d\351crit une ellipse" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 1415 "restart;\nwith(plots):\nN2:=V->sqrt(V[1]^2+V[2]^2 ):\n\nellipseAP:= proc(aa,bb)\n local u,U,a,b,t,u0,k,A,B,E,C,D,cerc le_B,cercle_D,tiges,courbe,arti,artiE,nbf,Cbar:\n if bb>aa then pri nt(\"le 2-i\350me param\350tre est le petit demi-axe doit \352tre inf \351rieur au 1-er\"):\n else\n Cbar:=0.7,0.2,0.2:\n b:=2*aa: a:=2*sqrt(aa^2-bb^2):\n U:=simplify([solve(( b*cos(t)-a-b*cos(w) ) ^2 + (b*sin(t)-b*sin(w) )^2-a^2,w)][2]):\n A:=[0,0]: D:=[a,0]: B:=[ b*cos(t),b*sin(t)]:\n cercle_B:=plot([op(B),t=0..2*Pi],color =grey, thickness=2):\n cercle_D:=plot([a+b*cos(w),b*sin(w),w=0..2*Pi],colo r =grey,thickness=2):\n C:=[a+b*cos(U),b*sin(U)]: \n E:=expand(D +u*(C-D)); u0:=solve(E[1]*B[2]-E[2]*B[1],u);\n E:=simplify(subs(u=u 0,E));\n nbf:=20:\n arti:=display([seq(PLOT(POINTS(op(evalf( subs(t=j*2*Pi/nbf,[A,B,C,D]))),\n COLOR(RGB ,0,0,0),SYMBOL(CIRCLE,12))),j=0..nbf)],insequence=true):\n arti E:=display([seq(PLOT(POINTS(op(evalf(subs(t=j*2*Pi/nbf,[E]))),\n \+ COLOR(RGB,1,0,0),SYMBOL(BOX,12))),j=0..nbf)],ins equence=true):\n tiges:=display([seq(PLOT(CURVES(evalf(subs(t=j *Pi*2/nbf,[A,B,C,D])),\n COLOR(RGB,Cbar),TH ICKNESS(3))),j=0..nbf)],insequence=true):\n courbe:=animate([op (subs(t=t*w,E)),t=0..2*Pi],w=0..1,frames=nbf+1,color=red):\n di splay([cercle_B,cercle_D,arti,artiE,tiges,courbe],axes=none):#\n\n \+ fi;\nend:" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoor ds has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 " ellipseAP(4,3);" }{TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 302 216 216 {PLOTDATA 2 "6&-%(ANIMATEG677(-%'POINTSG6(7$$\"\"!F,F+7$$\"\")F,F+ 7$$\"+i-:H8!\")F+7$$\"+AE]\"H&!\"*F+-%&COLORG6&%$RGBGF,F,F,-%'SYMBOLG6 $%'CIRCLEG\"#7-F(6%7$$\"+\\CvXmF7F+-F96&F;\"\"\"F,F,-F=6$%$BOXGF@-%'CU RVESG6%7&F*F-F0F4-F96&F;$\"\"(!\"\"$\"\"#FTFU-%*THICKNESSG6#\"\"$-FM6$ 7S7$$\"3%*=V168vXm!#i$=g`o/!\\F[o7$$\"3iz9\"\\Lfgm&F[o$\" 3C!*QrgTjZcF[o7$$\"3Oja0(fkJ*[F[o$\"3#>(phR_0HjF[o7$$\"3vUf/Xsh3SF[o$ \"3Ua`,64ABpF[o7$$\"3Ifmt:<6cIF[o$\"3-E![)3CD$R(F[o7$$\"3Ytr(4-4.-#F[o $\"3e3^e2XpSxF[o7$$\"3o)4#4e%4h2\"F[o$\"3Zy[*4*QHFzF[o7$$!3+'*QB>e&ox% !#?$\"3e.H&Qd)****zF[o7$$!3Y)>$R()e)**3\"F[o$\"3jvb4IyRDzF[o7$$!3qCdG? d%p6#F[o$\"3!z`X$Rg#[r(F[o7$$!3;.:&[9([=IF[o$\"3WB#e'GKp3uF[o7$$!3%z*z *)=A&Q.%F[o$\"3?9HYe![&3pF[o7$$!3)*\\[3\"e\"fJ[F[o$\"3CI&=2.%=wjF[o7$$ !3/'R6u2`9n&F[o$\"3PZSH[w@UcF[o7$$!3[l?WkLOBjF[o$\"3*pO\\u!z^+\\F[o7$$ !3hC#[=RXu#pF[o$\"3SNYfFBJ,SF[o7$$!3Ui\"4&=!\\ZQ(F[o$\"3%Q$*efL-m2$F[o 7$$!3`DJ_2))*3t(F[o$\"3%\\v\"Hh]Zd?F[o7$$!3`\"eLb,Cc#zF[o$\"3WM;//+M)3 \"F[o7$$!3/3mUF:'***zF[o$\"3#)zP>\\v/\"[#!#>7$$!3-U%y\\T]n#zF[o$!3;u#f \\[0,3\"F[o7$$!3fTG!QP_#RxF[o$!3MG/iAk#e-#F[o7$$!3p@lUq(41T(F[o$!3w2[0 H)yP,$F[o7$$!3&*>'yc!*[$RpF[o$!3I@G;4Fj!)RF[o7$$!3gQR-?MDL5F[o$!3_9Z X%f$*H$zF[o7$$!3S.V\\Vn!fW#F]w$!3;&))Q&4E'***zF[o7$$\"3A%y0Hgy,.\"F[o$ !3K(zngZ$RLzF[o7$$\"3\"e9jl2LS/#F[o$!3u'yuNqjWt(F[o7$$\"3Q2jW3(Q'oIF[o $!3[ilt`<1)Q(F[o7$$\"3*)*3y3YSE+%F[o$!3!Q#[W)3ym#pF[o7$$\"3O*f!f>.[()[ F[o$!3Bj\"zM$eWLjF[o7$$\"3E$3u\"4.WzcF[o$!3yc3Z[w6oH,q%RpF[o$!3mbQ1y:U!)RF[o7$$\"3CmEdi2+! 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{MPLTEXT 1 0 1362 "with(plots):\nellipseD:= proc(a,b) \n local u,t,w,A,B,E,C,tig es,courbe,arti,nbf,d,L,M,D1,r,m,m1,Cbar:\n Cbar:=0.7,0.2,0.2:\n r:=b: \n d:=-2*r: m1:=r-d: m:=m1*(b+a)/b/2:\n A: =[0,0]: B:=[r*cos(t),r*sin(t)] : \n L:= [r*cos(t)-sqrt(m1^2-(d- r*sin(t))^2),d] :\n M:= [r*cos(t)+sqrt(m1^2-(d-r*sin(t))^2),d] \+ :\n C:= simplify(evalf(expand(B+m/m1*(L-B)))) :\n D1:= s implify(evalf(expand(B+m/m1*(M-B)))) : \n E:= simplify(evalf(e xpand(D1+m/m1*(L-B))));\n nbf:=15:\n arti:=display([seq( PLOT(POINTS(op(evalf(subs(t=j*2*Pi/nbf,[A,C,B,E,L,M,D1]))),\n \+ COLOR(RGB,0,0,0),SYMBOL(CIRCLE,12))),j=0..nbf)],ins equence=true):\n if a>b then\n tiges:=display([seq(PL OT(CURVES(evalf(subs(t=j*Pi*2/nbf,[A,B,C,E,D1,B])),\n \+ COLOR(RGB,Cbar),THICKNESS(3))),j=0..nbf)],insequence=true): \n else\n tiges:=display([seq(PLOT(CURVES(evalf(su bs(t=j*Pi*2/nbf,[A,B,L,C,E,D1,M,B])),\n COL OR(RGB,Cbar),THICKNESS(3))),j=0..nbf)],insequence=true):\n fi;\n courbe:=animate([op(subs(t=t*w,E)),t=0..2*Pi],w=0..1,frames=nb f+1):\n display([plot([[-m,d],[m,d]],color=grey,thickness=2),\n plot([r],t=0..2*Pi,coords=polar,color=grey,thickness= 2),\n arti,tiges,courbe],axes=none):#\n \nend:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "ellipseD(2,4);" }}{PARA 13 " " 1 "" {GLPLOT2D 346 234 234 {PLOTDATA 2 "6&-%(ANIMATEG627'-%'POINTSG6 +7$$\"\"!F,F+7$$!+MR?3F!\"*$!\"'F,7$$\"\"%F,F+7$F4$!#7F,7$$!+5>FW\\F0$ !\")F,7$$\"+\">FWH\"F=F<7$$\"+$R?32\"F=F1-%&COLORG6&%$RGBGF,F,F,-%'SYM BOLG6$%'CIRCLEG\"#7-%'CURVESG6%7*F*F3F9F-F6FAF>F3-FE6&FG$\"\"(!\"\"$\" \"#FUFV-%*THICKNESSG6#\"\"$-FN6$7SF6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6 F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6F6-%'COLOU RG6&FG$\"*++++\"F=F+F+-FN6%7$7$$F0F,F<7$$\"\"*F,F<-Fjn6&FG$\")=THvF=Fh oFho-FY6#FW-FN6%7SF37$$\"3)zqV(\\\\aiR!#<$\"3-cSn=F6ha!#=7$$\"3+8>3S3_ pQFbp$\"387vs\"e:L,\"Fbp7$$\"3QS#3GfM%*p$Fbp$\"3:+\"po7W7_\"Fbp7$$\"3/ 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35 " Ellipsograp he par cercle directeur" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 140 "tige A B et parall\351logramme CLBM, E l'intersection de AB et LM : A et C f ixes : E d\351crit une ellipse de demi-axes AB/2 et sqrt(AB^2-AC^2) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 823 "with(plots):\nN2:=V->s qrt(V[1]^2+V[2]^2):\n \nellipseCD:= proc(a,b)\n local u,t,w,w0,k,A, B,E,C,c,BC,L,tigeAB,para,M,M1,Cbar,courbe,arti,artiE,nbf:\n if b>a \+ then print(\"le 2-i\350me param\350tre est le petit demi-axe doit \352 tre inf\351rieur au 1-er\"):\n else\n nbf:=21:#mettre un nom bre IMPAIR\n c:=sqrt(a^2-b^2): Cbar:=0.7,0.2,0.2:\n A:= [0,0]; B:=[2*a*cos(t),2*a*sin(t)] ; C:= [2*c,0] ;\n BC:=expand( B-C): BC:=simplify([BC[1]/N2(BC),BC[2]/N2(BC)]);\n L:=simplify( expand((B+C)*0.5+sqrt((a+c)^2-N2(expand((B-C)/2))^2)*[-BC[2],BC[1]])): \n M:=simplify(expand((B+C)*0.5-sqrt((a+c)^2-N2(expand((B-C))/2 )^2)*[-BC[2],BC[1]])):\n M1:=simplify(expand(L+4*sqrt(a*c)*(M-L )/N2(expand(M-L)))):\n E:=expand(L+w*(M-L)):w0:=simplify(solve( E[2]*B[1]-E[1]*B[2],w));\n E:=simplify(subs(w=w0,E)):" }}{PARA 12 "> " 1 "" {MPLTEXT 1 0 928 " arti:=display([seq(PLOT(POINTS( op(evalf(subs(t=j*2*Pi/nbf,[A,B,C,L,M]))),\n \+ COLOR(RGB,0,0,0),SYMBOL(CIRCLE,12))),j=0..nbf)],insequence=true):\n \+ artiE:=display([seq(PLOT(POINTS(op(evalf(subs(t=j*2*Pi/nbf,[E])) ),\n COLOR(RGB,1,0,0),SYMBOL(CIRCLE,12))),j =0..nbf)],insequence=true):\n tigeAB:=display([seq(PLOT(CURVES( evalf(subs(t=j*Pi*2/nbf,[A,B])),\n COLOR(RG B,Cbar),THICKNESS(3))),j=0..nbf)],insequence=true):\n para:=dis play([seq(PLOT(CURVES(evalf(subs(t=j*Pi*2/nbf,[L,C,M,B,L,M1])),\n \+ COLOR(RGB,Cbar),THICKNESS(3))),j=0..nbf)],inseq uence=true):\n courbe:=animate([op(subs(t=t*w,E)),t=0..2*Pi],w= 0..1,frames=nbf+1):\n print(display([plot([op(B),t=0..2*Pi],col or=black),\n arti,artiE,para,tigeAB,courbe],axes =none))\n#[plot([op(E),t=0..2*Pi],color=green),\n fi;\nend:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "ellipseCD(3,2);" }{TEXT -1 0 "" 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