{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 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 "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 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 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 P lot" -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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 156 "restart:a:=1:b:=ran d(0..100)()/10.;c:=rand(0..100)()/10.;mini:=floor(10*max(2*a-b-c,-2*a+ b+c,-2*a-b+c));maxi:=floor(10*(2*a+b+c));d:=rand(mini..maxi)()/10.;" } }{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been \+ redefined\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG$\"+++++q!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG$\"+++++w!\"*" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%%miniG\"$E\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%% maxiG\"$m\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG$\"++++I9!\")" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "a:=1:b:=0.8;c:=3;mini:=max( 2*a-b-c,-2*a+b-c,-2*a-b+c);maxi:=2*a+b+c;d:=(mini+maxi)/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG$\"\")!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%miniG $\"\"#!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%maxiG$\"#e!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG$\"+++++I!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "a:=2:b:=1.8;c:=1.1;mini:=max(2*a-b-c,-2*a +b-c,-2*a-b+c);maxi:=2*a+b+c;d:=(mini+maxi)/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG$\"#=!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"cG$\"#6!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%miniG$\"#6!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%maxiG$\"#p!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG$\"+++++S!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 741 "pi:=ev alf(Pi):n:=40:e:=1:th:=0:\nt:=fsolve((2*a+b*cos(th+tt)-c*cos(th-tt))^2 +(b*sin(th+tt)-c*sin(th-tt))^2=d^2,tt=0..pi);quad[0]:=plot([[a,0],[a+b *cos(th+t),b*sin(th+t)],[-a+c*cos(th-t),c*sin(th-t)],[-a,0],[a,0]],col or=black,axes=none):th0:=th: \nfor k to n+1 do\nprint(k,th*180/pi,t*18 0/pi):\nM[k]:=[a+b*cos(th+t),b*sin(th+t)]:N[k]:=[-a+c*cos(th-t),c*sin( th-t)]:\nR[k]:=(M[k]+N[k])/2:U[k]:=(M[k]-N[k])/2:V[k]:=[-U[k][2],U[k][ 1]]:\nquad[k]:=display(plot([[[a,0],M[k],N[k],[-a,0],[a,0]],[M[k]+V[k] ,M[k]-V[k]],[N[k]+V[k],N[k]-V[k]],[R[k]+V[k],R[k]-V[k]]],color=black,a xes=none,thickness=3),pointplot([[0,0],(M[k]+N[k])/2]),symbol=circle) \+ 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:\npi:=evalf(Pi):n:=80:e:=1:th:=3*pi/2.14:\nt:=fsolve((2*a+b*cos(th+tt )-c*cos(th-tt))^2+(b*sin(th+tt)-c*sin(th-tt))^2=4*d^2,tt=0..2*pi):quad [0]:=plot([[a,0],[a+b*cos(th+t),b*sin(th+t)],[-a+c*cos(th-t),c*sin(th- t)],[-a,0],[a,0]],color=black,axes=none):th0:=th: \nfor k to n do\npri nt(k,th*180/pi,t*180/pi):\nM[k]:=[a+b*cos(th+t),b*sin(th+t)]:N[k]:=[-a +c*cos(th-t),c*sin(th-t)]:\nR[k]:=(M[k]+N[k])/2:U[k]:=(M[k]-N[k])/2:V[ k]:=[-U[k][2],U[k][1]]:\nquad[k]:=display(plot([[[a,0],M[k],N[k],[-a,0 ]],[M[k],R[k]+r*V[k],N[k]]],color=black,axes=none,thickness=3),pointpl ot([[0,0],(M[k]+N[k])/2]),symbol=circle) :\nth:=th0+k*pi/n:t:=fsolve(( 2*a+b*cos(th+tt)-c*cos(th-tt))^2+(b*sin(th+tt)-c*sin(th-tt))^2=4*d^2,t t=t-e..t+e)\nod:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG#\"\"%\"\"$ " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG#\"\"%\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG#\"\"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"$\"+'[kL_#!\"($\"+CUIc>F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6% 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Pi):n:=80:e:=2:th:=3*pi/2.14:\nt:=fsolve((2*a+b*cos(th+tt)-c*cos(th-tt ))^2+(b*sin(th+tt)-c*sin(th-tt))^2=4*d^2,tt=0..2*pi):quad[0]:=plot([[a ,0],[a+b*cos(th+t),b*sin(th+t)],[-a+c*cos(th-t),c*sin(th-t)],[-a,0],[a ,0]],color=black,axes=none):th0:=th: \nfor k to n do\nprint(k,th*180/p i,t*180/pi):\nM[k]:=[a+b*cos(th+t),b*sin(th+t)]:N[k]:=[-a+c*cos(th-t), c*sin(th-t)]:\nR[k]:=(M[k]+N[k])/2:U[k]:=(M[k]-N[k])/2:V[k]:=[-U[k][2] ,U[k][1]]:\nquad[k]:=display(plot([[[a,0],M[k],N[k],[-a,0]],[M[k],R[k] +r*V[k],N[k]]],color=black,axes=none,thickness=3),pointplot([[0,0],(M[ k]+N[k])/2]),symbol=circle) :\nth:=th0+k*pi/n:t:=fsolve((2*a+b*cos(th+ tt)-c*cos(th-tt))^2+(b*sin(th+tt)-c*sin(th-tt))^2=4*d^2,tt=t-e..t+e)\n od:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG#\"\"%\"\"$" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"cG#\"\"%\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG#\"\"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"$\"+' [kL_#!\"($\"+CUIc>F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"#$\"+'[kea #!\"($\"+.(fL&>F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"$$\"+'[k$oD! \"($\"+L+#4&>F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%$\"+'[k3f#!\"( $\"+eV$*[>F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&$\"+'[kLh#!\"($\" +0UOZ>F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"'$\"+'[kej#!\"($\"+*)3 =Y>F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"($\"+'[k$eE!\"($\"+aPOX>F &" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\")$\"+'[k3o#!\"($\"+,!**[%>F& " }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"*$\"+'[kLq#!\"($\"+[*yZ%>F&" } }{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#5$\"+'[kes#!\"($\"+G;+X>F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#6$\"+'[k$[F!\"($\"+$pqb%>F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#7$\"+'[k3x#!\"($\"+,c\\Y>F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#8$\"+'[kLz#!\"($\"+.@zZ>F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#9$\"+'[ke\"G!\"($\"+:J[\\>F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#:$\"+'[k$QG!\"($\"+G+g^>F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#;$\"+'[k3'G!\"($\"+/Z=a>F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#<$\"+'[kL)G!\"($\"+qBHd>F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#=$\"+'[ke!H!\"($\"+!)f*4'>F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#>$\"+'[k$GH!\"($\"+SGRl>F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#?$\"+'[k3&H!\"($\"+&4:1(>F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#@$\"+'[kL(H!\"($\"+mq%o(>F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#A$\"+'[ke*H!\"($\"+DdN%)>F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#B$\"+'[k$=I!\"($\"+o'[N*>F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#C$\"+'[k3/$!\"($\"+cu40?F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#D$\"+'[kL1$!\"($\"+'>Y--#F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#E$\"+'[ke3$!\"($\"+kV#=/#F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#F$\"+'[k$3J!\"($\"+h " 0 "" {MPLTEXT 1 0 223 "m:=27:display(plot([[a+b*cos(tt),b *sin(tt),tt=Pi/2..3*Pi/2],[-a+c*cos(tt),c*sin(tt),tt=-Pi/2..Pi/2]],col or=blue),plot([[seq(R[k]+r*V[k],k=1..m)]],color=red),display(seq(quad[ k],k=1..m),insequence=true),scaling=constrained);" }}{PARA 13 "" 1 "" {GLPLOT2D 275 401 401 {PLOTDATA 2 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0 "" {MPLTEXT 1 0 49 "a :=1:k:=3:b:=a*k/3:c:=b:d:=b:r:=evalf(sqrt(3)/2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 223 "\n u:=simplify([solve(( b*cos(t)-a-c*cos( w) )^2 + (b*sin(t)-c*sin(w) )^2-d^2,w)]):\n B:=[0,0]: C:=[a,0]:\n \+ A:=[b*cos(t),b*sin(t)]:\n cercle_A:=plot([op(A),t=0..2*Pi],color \+ =blue): \n u1:=u[1]:u2:=u[2]:\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "D1:=[a+c*cos(u1),c*sin(u1)]:D2:=[a+c*cos(u2),c*s in(u2)]:\nU1:=(D1-A):U2:=(D2-A):\n " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 253 "V1:=[-U1[2],U1[1]]: V2:=[-U2[2],U2[1]]:\n M1:=( A+D1)/2+V1*r: M2:=(A+D2)/2+V2*r:\n lieu_M1:=plot([op(M1),t=0..2*Pi] ,color =red):\n lieu_M2:=plot([op(M2),t=0..2*Pi],color =green):\n \+ cercle_D:=plot([a+c*cos(w),c*sin(w),w=0..2*Pi],color =blue):\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 715 "n:=30:display([cercle_A, cercle_D,lieu_M1,lieu_M2,\n display([\n display([se q(display(\n PLOT(CURVES(evalf(subs(t=k*Pi/n,[ B,A,D1,C]) ) ),COLOR(RGB,0,0,0)),\n PLOT(CURVE 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D1:=[a+c*cos(u1),c*sin(u1)]:D2:=[a+c*cos(u2),c* sin(u2)]:\n U1:=(D1-A):U2:=(D2-A):\n \n V1:=[-U1[2],U1[1]]: V2:=[-U2 [2],U2[1]]:\n M1:=(A+D1)/2+V1: M2:=(A+D2)/2+V2:\n lieu_M1:=p lot([op(M1),t=0..2*Pi],color =red):\n lieu_M2:=plot([op(M2),t=0.. 2*Pi],color =green):\n cercle_D:=plot([a+c*cos(w),c*sin(w),w=0..2 *Pi],color =blue):\n \n n:=30:\n display([cercle_A,cercle_D,lieu_M1,li eu_M2,\n display([\n display([seq(display(\n \+ PLOT(CURVES(evalf(subs(t=k*Pi/n,[B,A,D1,C]) ) ),COLO R(RGB,0,0,0)),\n PLOT(CURVES(evalf(subs(t=k*Pi /n,[A,M1,D1]) ) ),COLOR(RGB,1,0,0) ) ),k=-n..n)],\n \+ insequence=true,thickness=2),\n display([seq(display( \n PLOT(CURVES(evalf(subs(t=k*Pi/n,[B,A,D2,C]) ) ),COLOR(RGB,0,0,0)),\n PLOT(CURVES(evalf(su bs(t=k*Pi/n,[A,M2,D2]) ) ),COLOR(RGB,0,1,0) )),k=n..3*n)],\n \+ insequence=true,thickness=2)],\n \+ insequence=true)], scaling=constrained,axes=none); \n \n \n" }} {PARA 7 "" 1 "" {TEXT -1 33 "Warning, computation interrupted\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "10 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }