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mf&y+\"F47$$!3a?1)3od!RHFA$\"3#HDBhB$\\.5F47$$!3,/qbf:W8RFA$\"3*Qgz$z_ '>+\"F47$$!3siQWIuZkeFA$\"3zLzojN(3+\"F47$$!3,K'*RR([m\"yFA$\"3LN4b+9 \\+5F47$$!3K/#=%)o7A<\"F1$\"32vb'pS=-+\"F47$$!3'*Q,@$> " 0 "" {MPLTEXT 1 0 605 "a:=-0.4:b:=sqrt(2*a+1)+1:r: =sqrt(a^2+b^2):aa:=min(2*a-2*r,-1):bb:=max(2*a+2*r,2):\ncc:=min(2*b-2* r,-2):dd:=max(2*b+2*r,2)+1:\nf1:=t->if cos(t)=0 then 10 else 1/cos(t) \+ fi:f2:=t->2*a*cos(t)+2*b*sin(t):f:=f1+f2:\nC1:=[f(t),t,t=-Pi/2+0.1..Pi /2-0.1]:C2:=[1/f(t),t,t=0..2*Pi]:C3:=[1,t,t=0..2*Pi]:\nbase1:=display( polarplot(C1,color=red),pointplot([0,0]),testplot([0,0,'O'],font=[TIME S,ITALIC,12])):\nbase2:=plot([[-1,t,t=cc..dd],[1,t,t=cc..dd],[2,t,t=cc ..dd],[a+r*cos(t),b+r*sin(t),t=0..2*Pi],[2*a+2*r*cos(t),2*b+2*r*sin(t) ,t=0..2*Pi],[t,0,t=aa..bb],[0,t,t=cc..dd]],color=[blue$5,black$2],line style=[2$2,1,2,1,2$2]):" }}{PARA 8 "" 1 "" {TEXT -1 144 "Error, (in di splay) invalid argument testplot([0, 0, O],font = [TIMES, ITALIC, 12]) which must be a plot structure, or a list/set/array thereof\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 322 "n:=30:display([base1,base2, \ndisplay(\n[seq(\ndisplay([plot([[[0,0],[f(tt)*cos(tt),f(tt)*sin(tt)] ]$2,[[2*f1(tt)*cos(tt),2*f1(tt)*sin(tt)],[2*f2(tt)*cos(tt),2*f2(tt)*si n(tt)]]$2],style=[line,point,line,point],color=black,symbol=[box,circl e,box$2])]),tt=seq(k*Pi/n,k=0..n-1))],insequence=true)],axes=none,view =[aa..bb,cc..dd]);" }{TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%(ANIMATEG6@70-%'CURVESG6&7$7$$\"\"!F-F,7$$\"3 5+++++++?!#=F,-%&STYLEG6#%%LINEG-%'SYMBOLG6#%$BOXG-%'COLOURG6&%$RGBGF- F-F--F(6&F*-F36#%&POINTG-F76#%'CIRCLEGF:-F(6&7$7$$\"\"#F-F,7$$!33+++++ ++;!#g&F1$!3givK\"*36 bPFO7$$\"3Y52]!Q.57&F1$!3-^GR^eC#4$FO7$$\"3s\"**HA!He'G%F1$!3;q8')R?% \\?#FO7$$\"3[^J#z!R\\dMF1$!3y&o]\\oBoa\"FO7$$\"3i&RQ(zE\\D;F1$!3+MbfSX (pf&F17$$!3;i_v4`:\"\\\"!#>$\"3\"*ylP;b')QTFcq7$$!3RpsjB40==F1$\"3MA2# *eZM)>%F17$$!3Gq^o\"[ycD$F1$\"3yeh[2m;ekF17$$!3z%\\Yi3'o6YF1$\"3Gp*H19 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87$$!3#3fcH.F\">WF8$!3ei[fu4x3=F87$$!3#R'==a&)R%f$F8$!3g0bI(z8nv\"F87$ $!3%=_:cgi:!GF8$!3m^M\"=P]6g\"F87$$!3_.+#F8$!3%Qfj!\\MEI8F87$$!3 YQ_.]#G*p7F8$!3m;!>ME1Yp*F47$$!35.DnI&>)zdF4$!3Qad\"*)y>b0&F47$$\"3TK?F87$$\"3e_6r*o ')*R;F8$\"3!)*RS\"))pSD8,O@ZWF8F;F_\\lFe\\lFh\\lFb\\mF]]m-%*AXESSTYLEG6#%%NONEG-F`\\l6 $Fb\\lFb\\l-Ff\\l6$;$!+7+&H!Q!\"*$\"+7+&H?#Fiebl;$!\"$F-$\"+/sP(*yFieb l" 1 2 0 1 10 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" " Curve 2" "Curve 3" "Curve 4" "Curve 5" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "programme g\351n\351ral cissoidale cercle droite" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 535 "a:=1.1:b:=sqrt(2*a+1)-1:r:= sqrt(a^2+b^2):aa:=min(2*a-2*r,-1):bb:=max(2*a+2*r,2):\ncc:=min(2*b-2*r ,-2):dd:=max(2*b+2*r,2)+1:\nf1:=t->if cos(t)=0 then 10 else 1/cos(t) f i:f2:=t->2*a*cos(t)+2*b*sin(t):f:=f1+f2:\nC1:=[f(t),t,t=-Pi/2+0.1..Pi/ 2-0.1]:C2:=[1/f(t),t,t=0..2*Pi]:C3:=[1,t,t=0..2*Pi]:\nbase1:=polarplot (C1,color=red):\nbase2:=plot([[-1,t,t=cc..dd],[1,t,t=cc..dd],[2,t,t=cc ..dd],[a+r*cos(t),b+r*sin(t),t=0..2*Pi],[2*a+2*r*cos(t),2*b+2*r*sin(t) ,t=0..2*Pi],[t,0,t=aa..bb],[0,t,t=cc..dd]],color=[blue$5,black$2],line style=[2$2,1,2,1,2$2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 322 "n:=30:display([base1,base2,\ndisplay(\n[seq(\ndisplay([plot([[[0,0],[ f(tt)*cos(tt),f(tt)*sin(tt)]]$2,[[2*f1(tt)*cos(tt),2*f1(tt)*sin(tt)],[ 2*f2(tt)*cos(tt),2*f2(tt)*sin(tt)]]$2],style=[line,point,line,point],c olor=black,symbol=[box,circle,box$2])]),tt=seq(k*Pi/n,k=0..n-1))],inse quence=true)],axes=none,view=[aa..bb,cc..dd]);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "inverse de conique" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "polarplot([C1,C2,C3],view=[-1..4,-2 ..4],color=[red,blue,black],axes=none,linestyle=[1$2,2$2]);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 371 "with(linalg):\nx:=t->2.*a+1 -t^2:\ny:=t->2.*t+2*b:\nx1:=D(x):y1:=D(y):n:=sqrt(x1^2+y1^2):\nu:=[x1( t)/n(t),y1(t)/n(t)]:\nM:=[x(t),y(t)]:\nH:=M-dotprod(M(t),u)*u:\nu:=3:n :=20:\nL:=seq(plot([[0,0],H,M],color=black),t=seq(-u+k*2*u/n,k=0..n)): \ndisplay([display(L,insequence=true),plot([[x,y,-u..u],[[2*a,2*b]]],s tyle=[line,point],color=blue),base1],view=[aa..bb,cc-1..dd+1],axes=non e);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "cissoide" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 550 "a:=1.87:b:=sqrt(2*a+1):r:=sqrt(a^2+b^2): aa:=min(2*a-2*r,-1):bb:=max(2*a+2*r,2):\ncc:=min(2*b-2*r,-2)-1:dd:=max (2*b+2*r,2)+2:\nf1:=t->if cos(t)=0 then 10 else 1/cos(t) fi:f2:=t->2*a *cos(t)+2*b*sin(t):f:=f1+f2:\nC1:=[-f(t),t,t=-Pi/2+0.1..Pi/2-0.1]:C2:= [-1/f(t),t,t=0..2*Pi]:C3:=[-1,-t,t=0..2*Pi]:\nbase1:=polarplot(C1,colo r=red):\nbase2:=plot([[1,-t,t=cc..dd],[-1,-t,t=cc..dd],[-2,-t,t=cc..dd ],[-a-r*cos(t),-b-r*sin(t),t=0..2*Pi],[-2*a-2*r*cos(t),-2*b-2*r*sin(t) ,t=0..2*Pi],[-t,0,t=aa..bb],[0,-t,t=cc..dd]],color=[blue$5,black$2],li nestyle=[2$2,1,2,1,2$2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 334 "n:=30:display([base1,base2,\ndisplay(\n[seq(\ndisplay([plot([[[0, 0],[-f(tt)*cos(tt),-f(tt)*sin(tt)]]$2,[[-2*f1(tt)*cos(tt),-2*f1(tt)*si n(tt)],[-2*f2(tt)*cos(tt),-2*f2(tt)*sin(tt)]]$2],style=[line,point,lin e,point],color=black,symbol=[box,circle,box$2])]),tt=seq(k*Pi/n,k=0..n -1))],insequence=true)],axes=none,view=[-aa..-bb,-cc+1..-dd]);" } {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "inverse de coniqu e" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "polarplot([C1,C2,C3],v iew=[1..-7,4..-7],color=[red,blue,black],axes=none,linestyle=[1$2,2$2] );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 374 "with(linalg):\nx:=t- >-(2.*a+1-t^2):\ny:=t->-(2.*t+2*b):\nx1:=D(x):y1:=D(y):n:=sqrt(x1^2+y1 ^2):\nu:=[x1(t)/n(t),y1(t)/n(t)]:\nM:=[x(t),y(t)]:\nH:=M-dotprod(M(t), u)*u:\nu:=3:n:=20:\nL:=seq(plot([[0,0],H,M],color=black),t=seq(-u+k*2* u/n,k=0..n)):\ndisplay([display(L,insequence=true),plot([[x,y,-u..u],[ [-2*a,-2*b]]],style=[line,point],color=blue),base1],view=[-7..2,-10..2 ],axes=none);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "strophoid" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 520 "a:=-1:b:=1:r:=sqrt(a^2+b^2) :aa:=min(2*a-2*r,-1):bb:=max(2*a+2*r,2):\ncc:=min(2*b-2*r,-2):dd:=max( 2*b+2*r,2)+1:\nf1:=t->if cos(t)=0 then 10 else 1/cos(t) fi:f2:=t->2*a* cos(t)+2*b*sin(t):f:=f1+f2:\nC1:=[f(t),t,t=-Pi/2+0.1..Pi/2-0.1]:C2:=[1 /f(t),t,t=0..Pi]:C3:=[1,t,t=0..2*Pi]:\nbase1:=polarplot(C1,color=red): \nbase2:=plot([[-1,t,t=cc..dd],[1,t,t=cc..dd],[2,t,t=cc..dd],[a+r*cos( t),b+r*sin(t),t=0..2*Pi],[2*a+2*r*cos(t),2*b+2*r*sin(t),t=0..2*Pi],[t, 0,t=aa..bb],[0,t,t=cc..dd]],color=[blue$5,black$2],linestyle=[2$2,1,2, 1,2$2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 322 "n:=30:display( [base1,base2,\ndisplay(\n[seq(\ndisplay([plot([[[0,0],[f(tt)*cos(tt),f (tt)*sin(tt)]]$2,[[2*f1(tt)*cos(tt),2*f1(tt)*sin(tt)],[2*f2(tt)*cos(tt ),2*f2(tt)*sin(tt)]]$2],style=[line,point,line,point],color=black,symb ol=[box,circle,box$2])]),tt=seq(k*Pi/n,k=0..n-1))],insequence=true)],a 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:=-1/2:b:=1:r:=sqrt(a^2+b^2):aa:=min(2*a-2*r,-1):bb:=max(2*a+2*r,2):\n cc:=min(2*b-2*r,-2):dd:=max(2*b+2*r,2)+1:\nf1:=t->if cos(t)=0 then 10 \+ else 1/cos(t) fi:f2:=t->2*a*cos(t)+2*b*sin(t):f:=f1+f2:\nC1:=[f(t),t,t =-Pi/2+0.1..Pi/2-0.1]:C2:=[1/f(t),t,t=0..Pi]:C3:=[1,t,t=0..2*Pi]:\nbas e1:=polarplot(C1,color=red):\nbase2:=plot([[-1,t,t=cc..dd],[1,t,t=cc.. dd],[2,t,t=cc..dd],[a+r*cos(t),b+r*sin(t),t=0..2*Pi],[2*a+2*r*cos(t),2 *b+2*r*sin(t),t=0..2*Pi],[t,0,t=aa..bb],[0,t,t=cc..dd]],color=[blue$5, black$2],linestyle=[2$2,1,2,1,2$2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 322 "n:=30:display([base1,base2,\ndisplay(\n[seq(\ndispla y([plot([[[0,0],[f(tt)*cos(tt),f(tt)*sin(tt)]]$2,[[2*f1(tt)*cos(tt),2* f1(tt)*sin(tt)],[2*f2(tt)*cos(tt),2*f2(tt)*sin(tt)]]$2],style=[line,po int,line,point],color=black,symbol=[box,circle,box$2])]),tt=seq(k*Pi/n ,k=0..n-1))],insequence=true)],axes=none,view=[aa..bb,cc..dd]);" } {TEXT -1 0 "" }}{PARA 13 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "inverse de conique" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "polarplot([C1,C2,C3],view=[-2..2,-2..2],color=[red,bl ue,black],axes=none,linestyle=[1$2,2$2]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "podaire de parabole" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 371 "with(linalg): \nx:=t->2.*a+1-t^2:\ny:=t->2.*t+2*b:\nx1:=D(x):y1:=D(y):n:=sqrt(x1^2+y 1^2):\nu:=[x1(t)/n(t),y1(t)/n(t)]:\nM:=[x(t),y(t)]:\nH:=M-dotprod(M(t) ,u)*u:\nu:=3:n:=19:\nL:=seq(plot([[0,0],H,M],color=black),t=seq(-u+k*2 *u/n,k=0..n)):\ndisplay([display(L,insequence=true),plot([[x,y,-u..u], [[2*a,2*b]]],style=[line,point],color=blue),base1],view=[aa..bb,cc-1.. dd+1],axes=none);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "trisectrice" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 518 "a:=-2:b:=0:r:=sqrt(a^2+b^2):aa:=min(2*a-2*r,-1):bb:= max(2*a+2*r,2):\ncc:=min(2*b-2*r,-2):dd:=max(2*b+2*r,2):\nf1:=t->if co s(t)=0 then 10 else 1/cos(t) fi:f2:=t->2*a*cos(t)+2*b*sin(t):f:=f1+f2: \nC1:=[f(t),t,t=-Pi/2+0.1..Pi/2-0.1]:C2:=[1/f(t),t,t=0..Pi]:C3:=[1,t,t =0..2*Pi]:\nbase1:=polarplot(C1,color=red):\nbase2:=plot([[-1,t,t=cc.. dd],[1,t,t=cc..dd],[2,t,t=cc..dd],[a+r*cos(t),b+r*sin(t),t=0..2*Pi],[2 *a+2*r*cos(t),2*b+2*r*sin(t),t=0..2*Pi],[t,0,t=aa..bb],[0,t,t=cc..dd]] ,color=[blue$5,black$2],linestyle=[2$2,1,2,1,2$2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 322 "n:=30:display([base1,base2,\ndisplay(\n[ seq(\ndisplay([plot([[[0,0],[f(tt)*cos(tt),f(tt)*sin(tt)]]$2,[[2*f1(tt )*cos(tt),2*f1(tt)*sin(tt)],[2*f2(tt)*cos(tt),2*f2(tt)*sin(tt)]]$2],st yle=[line,point,line,point],color=black,symbol=[box,circle,box$2])]),t t=seq(k*Pi/n,k=0..n-1))],insequence=true)],axes=none,view=[aa..bb,cc.. dd]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "inverse d e conique" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "polarplot([C1, C2,C3],view=[-3..2,-2..2],color=[red,blue,black],axes=none,linestyle=[ 1$2,2$2]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "poda ire de parabole" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 371 "with(li nalg):\nx:=t->2.*a+1-t^2:\ny:=t->2.*t+2*b:\nx1:=D(x):y1:=D(y):n:=sqrt( x1^2+y1^2):\nu:=[x1(t)/n(t),y1(t)/n(t)]:\nM:=[x(t),y(t)]:\nH:=M-dotpro d(M(t),u)*u:\nu:=3:n:=20:\nL:=seq(plot([[0,0],H,M],color=black),t=seq( -u+k*2*u/n,k=0..n)):\ndisplay([display(L,insequence=true),plot([[x,y,- u..u],[[2*a,2*b]]],style=[line,point],color=blue),base1],view=[aa..bb, cc-1..dd+1],axes=none);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "visiera" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 503 "a:= 1/2:b:=0:r:=sqrt(a^2+b^2):aa:=min(2*a-2*r,-1):bb:=max(2*a+2*r,2):\ncc: =min(2*b-2*r,-2)-1:dd:=max(2*b+2*r,2)+1:\nf1:=t-> 1/cos(t):f2:=t->2*a* cos(t)+2*b*sin(t):f:=f1+f2:\nC1:=[f(t-Pi/2),t,t=0.1..Pi-0.1]:C2:=[1/f( t-Pi/2),t,t=0..2*Pi]:C3:=[1,t,t=0..2*Pi]:\nbase1:=polarplot([C1],color =red):\nbase2:=plot([[-t,-1,t=cc..dd],[t,1,t=cc..dd],[t,2,t=cc..dd],[b +r*cos(t),a+r*sin(t),t=0..2*Pi],[2*b+2*r*cos(t),2*a+2*r*sin(t),t=0..2* Pi],[0,t,t=aa..bb],[t,0,t=cc..dd]],color=[blue$5,black$2],linestyle=[2 $2,1,2,1,2$2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "display ([polarplot(C1,color=red),plot([[0,0]],style=point,symbol=circle)],vie w=[-4..4,0..2],scaling=constrained,axes=none);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 322 "n:=30:disp lay([base1,base2,\ndisplay(\n[seq(\ndisplay([plot([[[0,0],[f(tt)*sin(t t),f(tt)*cos(tt)]]$2,[[2*f1(tt)*sin(tt),2*f1(tt)*cos(tt)],[2*f2(tt)*si n(tt),2*f2(tt)*cos(tt)]]$2],style=[line,point,line,point],color=black, symbol=[box,circle,box$2])]),tt=seq(k*Pi/n,k=0..n-1))],insequence=true )],axes=none,view=[cc..dd,aa..bb]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "polarplot([C1,C2,C3],view=[-2..2,-2..2],color=[red,bl ue,black],axes=none,linestyle=[1$2,2$2]);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 299 "f:=t->2-0.25*t**2:\nff:=D(f):n:=sqrt(1+ff**2):\nu: =[1/n(t),ff(t)/n(t)]:\nM:=[t,f(t)]:\nH:=M-dotprod(M(t),u)*u:\nL:=seq(p lot([[0,0],H,[t,f(t)]],color=black),t=seq(-8+k*0.5,k=0..32)):\ndisplay ([display(L,insequence=true),plot(f,-5..5,color=blue),polarplot(sin(t) +1/sin(t),t=0.01..3.13)],view=[-5..5,-2..2]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 397 "w ith(linalg):\nx:=t->2.*a+1-t^2:\ny:=t->2.*t+2*b:\nx1:=D(x):y1:=D(y):n: =sqrt(x1^2+y1^2):\nu:=[y1(t)/n(t),x1(t)/n(t)]:\nM:=[y(t),x(t)]:\nH:=M- dotprod(M(t),u)*u:\nu:=3:n:=20:\nL:=seq(plot([[0,0],H,M],color=black), t=seq(-u+k*2*u/n,k=0..n)):\ndisplay([display(L,insequence=true),plot([ [y,x,-u..u],[[2*b,2*a]]],style=[line,point],color=blue),polarplot(sin+ 1/sin,0.01..3.13)],view=[cc-1..dd+1,aa..bb],axes=none);" }}{PARA 13 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "charpentie r" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 784 "restart:a:=0.5:\nu:=0 .5:\nx0:=-a:y0:=0:\nxh:=-a+2*a*cos(v):yh:=2*a*sin(v):\nxq:=a:yq:=2*a*( 1-cos(v))/sin(v):\nxp:=xq+x0-xh:yp:=yq+y0-yh:\nxm:=(u*xp+(1-u)*xq):ym: =(u*yp+(1-u)*yq):\nn:=20:\nb:=eval(yq-0.5,v=-Pi+0.001+4*Pi/n):\nc:=eva l(yq+0.5,v=-Pi+0.001+2*(n-2)*Pi/n):\ncourbe:=plot([ym,xm,v=-Pi+0.1..Pi -0.1]):\nanima:=display(seq(display([plot(eval([[[y0,x0],[yp,xp],[yq,x q]],[[ym,xm]]],v=-Pi+0.001+2*k*Pi/n),color=black,style=[line,point],sy mbol=circle),textplot(eval([yp,xp,'P'],v=-Pi+0.001+2*k*Pi/n),align=\{A BOVE,RIGHT\}),textplot(eval([yq,xq,'Q'],v=-Pi+0.001+2*k*Pi/n),align=\{ ABOVE,RIGHT\})])\n,k=2..n-2),insequence=true):\ndisplay([courbe,textpl ot([y0,x0,'O'],align=\{ABOVE,RIGHT\}),plot([[[b,a],[c,a]],[[0,-a]]],st yle=[line,point],symbol=circle,color=blue),anima],\nview=[b..c,-a..a+1 ],axes=none);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 784 "restart:a :=0.5:\nu:=0.8:\nx0:=-a:y0:=0:\nxh:=-a+2*a*cos(v):yh:=2*a*sin(v):\nxq: =a:yq:=2*a*(1-cos(v))/sin(v):\nxp:=xq+x0-xh:yp:=yq+y0-yh:\nxm:=(u*xp+( 1-u)*xq):ym:=(u*yp+(1-u)*yq):\nn:=20:\nb:=eval(yq-0.5,v=-Pi+0.001+4*Pi /n):\nc:=eval(yq+0.5,v=-Pi+0.001+2*(n-2)*Pi/n):\ncourbe:=plot([ym,xm,v =-Pi+0.1..Pi-0.1]):\nanima:=display(seq(display([plot(eval([[[y0,x0],[ yp,xp],[yq,xq]],[[ym,xm]]],v=-Pi+0.001+2*k*Pi/n),color=black,style=[li ne,point],symbol=circle),textplot(eval([yp,xp,'P'],v=-Pi+0.001+2*k*Pi/ n),align=\{ABOVE,RIGHT\}),textplot(eval([yq,xq,'Q'],v=-Pi+0.001+2*k*Pi /n),align=\{ABOVE,RIGHT\})])\n,k=2..n-2),insequence=true):\ndisplay([c ourbe,textplot([y0,x0,'O'],align=\{ABOVE,RIGHT\}),plot([[[b,a],[c,a]], [[0,-a]]],style=[line,point],symbol=circle,color=blue),anima],\nview=[ b..c,-a..a+1],axes=none);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 782 "restart:a:=0.5:\nu:=1:\nx0:=-a:y0:=0:\nxh:=-a+2*a*cos(v):yh:=2*a* sin(v):\nxq:=a:yq:=2*a*(1-cos(v))/sin(v):\nxp:=xq+x0-xh:yp:=yq+y0-yh: \nxm:=(u*xp+(1-u)*xq):ym:=(u*yp+(1-u)*yq):\nn:=20:\nb:=eval(yq-0.5,v=- Pi+0.001+4*Pi/n):\nc:=eval(yq+0.5,v=-Pi+0.001+2*(n-2)*Pi/n):\ncourbe:= plot([ym,xm,v=-Pi+0.1..Pi-0.1]):\nanima:=display(seq(display([plot(eva l([[[y0,x0],[yp,xp],[yq,xq]],[[ym,xm]]],v=-Pi+0.001+2*k*Pi/n),color=bl ack,style=[line,point],symbol=circle),textplot(eval([yp,xp,'P'],v=-Pi+ 0.001+2*k*Pi/n),align=\{ABOVE,RIGHT\}),textplot(eval([yq,xq,'Q'],v=-Pi +0.001+2*k*Pi/n),align=\{ABOVE,RIGHT\})])\n,k=2..n-2),insequence=true) :\ndisplay([courbe,textplot([y0,x0,'O'],align=\{ABOVE,RIGHT\}),plot([[ [b,a],[c,a]],[[0,-a]]],style=[line,point],symbol=circle,color=blue),an ima],\nview=[b..c,-a..a+1],axes=none);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 813 "restart:a:=0.5:\nu:=-1/2:\nx0:=-a:y0:=0:\nxh:=-a+2*a *cos(v):yh:=2*a*sin(v):\nxq:=a:yq:=2*a*(1-cos(v))/sin(v):\nxp:=xq+x0-x h:yp:=yq+y0-yh:\nxm:=(u*xp+(1-u)*xq):ym:=(u*yp+(1-u)*yq):\nn:=20:\nb:= eval(yq-0.5,v=-Pi+0.001+4*Pi/n):\nc:=eval(yq+0.5,v=-Pi+0.001+2*(n-2)*P i/n):\ncourbe:=plot([ym,xm,v=-Pi+0.1..Pi-0.1]):\nanima:=display(seq(di splay([plot(eval([[[y0,x0],[yp,xp],[yq,xq]],[[ym,xm],[yq,xq]],[[ym,xm] ]],v=-Pi+0.001+2*k*Pi/n),color=black,style=[line$2,point],symbol=circl e),textplot(eval([yp,xp,'P'],v=-Pi+0.001+2*k*Pi/n),align=\{ABOVE,RIGHT \}),textplot(eval([yq,xq,'Q'],v=-Pi+0.001+2*k*Pi/n),align=\{ABOVE,RIGH T\})])\n,k=2..n-2),insequence=true):\ndisplay([courbe,textplot([y0,x0, 'O'],align=\{ABOVE,RIGHT\}),plot([[[b-1,a],[c+1,a]],[[0,-a]]],style=[l ine,point],symbol=circle,color=blue),anima],\nview=[b-1..c+1,-a..a+1], axes=none);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 812 "restart:a:= 0.5:\nu:=2:\nx0:=-a:y0:=0:\nxh:=-a+2*a*cos(v):yh:=2*a*sin(v):\nxq:=a:y q:=2*a*(1-cos(v))/sin(v):\nxp:=xq+x0-xh:yp:=yq+y0-yh:\nxm:=(u*xp+(1-u) *xq):ym:=(u*yp+(1-u)*yq):\nn:=20:\nb:=eval(yq-0.5,v=-Pi+0.001+4*Pi/n): \nc:=eval(yq+0.5,v=-Pi+0.001+2*(n-2)*Pi/n):\ncourbe:=plot([ym,xm,v=-Pi +0.1..Pi-0.1]):\nanima:=display(seq(display([plot(eval([[[y0,x0],[yp,x p],[yq,xq]],[[ym,xm],[yq,xq]],[[ym,xm]]],v=-Pi+0.001+2*k*Pi/n),color=b lack,style=[line$2,point],symbol=circle),textplot(eval([yp,xp,'P'],v=- Pi+0.001+2*k*Pi/n),align=\{ABOVE,RIGHT\}),textplot(eval([yq,xq,'Q'],v= -Pi+0.001+2*k*Pi/n),align=\{ABOVE,RIGHT\})])\n,k=2..n-2),insequence=tr ue):\ndisplay([courbe,textplot([y0,x0,'O'],align=\{ABOVE,RIGHT\}),plot ([[[b-1,a],[c+1,a]],[[0,-a]]],style=[line,point],symbol=circle,color=b lue),anima],\nview=[b-1..c+1,-a-1..a+2],axes=none);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "7 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }