{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 }{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 "Heading 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 "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Ti mes" 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 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 18 "" 0 "" {TEXT -1 16 "Carr\351s articul\351s" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Alain Esculier - 10/2014" }}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 35 " utilitaires ( \340 ex\351cuter a u d\351but)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "with(plots): \n# produit scalaire\nps:=proc(U,V) \nlocal u,v; u:=expand(U): v:=expa nd(V):\n add(u[i]*v[i],i=1..nops(u)):\nend:" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 255 "# produit vectoriel\npv:=proc(u,v)\n local U,V; \+ U:=expand(u): V:=expand(v):\n[U[2]*V[3]-U[3]*V[2],U[3]*V[1]-U[1]*V[3], U[1]*V[2]-U[2]*V[1]]:\nend proc:\n#--------- normalisation d'un vecteu r -----\nVnorm:= U -> expand(U/sqrt(ps(U,U))):\nperp:=V -> [-V[2],V[1] ]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1898 "#======= rot 2D ====\nrot:= proc(t,pt) local ptr,xr,yr: #centre,\n ptr:=expand(pt): xr:=ptr [1]: yr:=ptr[2]: # ptr:=expand(pt-centre):\n expand( [cos(t)*xr-sin (t)*yr,sin(t)*xr+cos(t)*yr]): #centre+ \nend:\n#**************rotati ons \340 une liste de pt 2D******************************\nLrotO:=(t,L iste) -> if type(evalf(Liste[1,1]),numeric) then map( u ->rot(t,u),Li ste): else map( u->LrotO(t,u),Liste): fi:\n\nLrot:=(centre,t,Liste) -> if type(evalf(Liste[1,1]),numeric) then map( u ->rot(centre,t,u),Lis te): \n else map( u->Lrot(centre,t,u),Liste): fi:\nLtrans:=(V,Liste) -> if type(evalf(Liste[1,1]),numeric) then map ( u ->expand(u+V),Liste): \n else map( u->Ltrans( V,u),Liste) fi:\nLsymX:= Liste -> if type(evalf(Liste[1,1]),numeric) t hen map( u ->[u[1],-u[2]],Liste): else map( u->LsymX(u),Liste): fi:\nL symY:= Liste -> if type(evalf(Liste[1,1]),numeric) then map( u ->[-u[1 ],u[2]],Liste): else map( u->LsymY(u),Liste): fi:\n\n#******* tubeplot g\351n\351ralis\351 \340 une suite de lignes polygonale ********** \n tracelist:=proc(L,r,col) local p,t,u,i; \n if type(L[1,1],numeric) then p:=nops(L):\n tubeplot(\{seq(expand(L[i]+t*( L[ (i mod p) +1]-L[i])),i=1..nops(L))\},t=0..1,radius=r,grid=[2,10],style=patch nogrid,color=col),\n plot3d(\{seq(expand(L[i]+r*[cos(t)*sin(u) ,sin(t)*sin(u),cos(u)]),i=1..nops(L))\},t=0..2*Pi,u=0..Pi,grid=[6,12], style=patchnogrid,color=col):\n else op(map(u ->tracelist(u,r,col), L)): fi;\nend:\ntracelistouverte:=proc(L,r,col) local p,t,u,i; \n \+ if type(L[1,1],numeric) then p:=nops(L):\n tubeplot(\{seq(ex pand(L[i]+t*( L[ i +1]-L[i])),i=1..nops(L)-1)\},t=0..1,radius=r,grid=[ 2,10],style=patchnogrid,color=col),\n plot3d(\{seq(expand(L[i] +r*[cos(t)*sin(u),sin(t)*sin(u),cos(u)]),i=1..nops(L))\},t=0..2*Pi,u=0 ..Pi,grid=[6,12],style=patchnogrid,color=col):\n else op(map(u ->tr acelist(u,r,col),L)): fi;\nend:" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "carre_mobile(0,0,1)[3..4];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$7$,&-%$cosG6#\"\"\"F)-%$sinGF(F),&F&F)F*!\"\"7$,&F*F) F&F-F%" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 17 " carr\351s articul\351 s" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 522 "carre:=[[-1,-1],[1,-1] ,[1,1],[-1,1]]:\nrotcarre:= t -> LrotO(t,carre):\ncarre_mobile:=proc(i ,j,t)\n local tx,ty :\n tx:=2*i*sqrt(2)*cos(Pi/4-t): ty:=2*j*sqrt(2)*cos(Pi/4-t):\n Ltrans([tx,ty],rotcarre( (2*( (i+j) mod 2)-1)* t)):\nend:\nbasediag1:=t -> [carre_mobile(0,0,t)[1],c arre_mobile(0,0,t)[3]]:diag1:=proc(i,j,t) local tx,ty;\n tx:=2*i*sq rt(2)*cos(Pi/4-t): ty:=(2*j)*sqrt(2)*cos(Pi/4-t):\n Ltrans([tx,ty], basediag1(t)):\nend:\n\nbaseV1:=t -> [op(carre_mobile(0,0,t)[3..4]),ca rre_mobile(0,1,t)[2]]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 759 "triangle V1:=proc(i,j,t) local tx,ty;\n tx:=2*i*sqrt(2)*cos(Pi/4-t): ty:=(2* j)*sqrt(2)*cos(Pi/4-t):\n Ltrans([tx,ty],baseV1(t)):\nend:\nbaseV2: =t -> [op(carre_mobile(1,0,t)[3..4]),carre_mobile(1,1,t)[1]]:\ntriangl eV2:=proc(i,j,t) local tx,ty;\n tx:=(2*i)*sqrt(2)*sin(Pi/4+t): ty:= (2*j)*sqrt(2)*sin(Pi/4+t):\n Ltrans([tx,ty],baseV2(t)):\nend:\n\nba seH1:=t -> [op(carre_mobile(0,0,t)[2..3]),carre_mobile(1,0,t)[1]]:\ntr iangleH1:=proc(i,j,t) local tx,ty;\n tx:=2*i*sqrt(2)*cos(Pi/4-t): t y:=(2*j)*sqrt(2)*cos(Pi/4-t):\n Ltrans([tx,ty],baseH1(t)):\nend:\nb aseH2:=t -> [op(carre_mobile(0,1,t)[2..3]),carre_mobile(1,1,t)[4]]:\nt riangleH2:=proc(i,j,t) local tx,ty;\n tx:=(2*i)*sqrt(2)*sin(Pi/4+t) : ty:=(2*j)*sqrt(2)*sin(Pi/4+t):\n Ltrans([tx,ty],baseH2(t)):\nend: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 978 "n:=3;\ndispo:=proc(p,k ) global n:\n display([polygonplot([seq(seq(carre_mobile(i,j,Pi/p*k), i=0..n),j=0..n)],color=cyan), polygonplot([seq(seq(o p([triangleV2(2*i,2*j,Pi/p*k)]),i=0..n/2),j=0..n/2)] ,color=blue),\n \+ polygonplot([seq(seq(op([triangleV2(2*i+1,2*j+1,Pi/p*k)]),i=0.. n/2),j=0..n/2)] ,color=blue),\n polygonplot([seq(seq(op([trian gleV1(2*i,2*j,Pi/p*k)]),i=0..n/2),j=0..n/2)] ,color=red),\n po lygonplot([seq(seq(op([triangleV1(2*i+1,2*j+1,Pi/p*k)]),i=0..n/2),j=0. .n/2)] ,color=red),\n\n polygonplot([seq(seq(op([triangleH1(2* i,2*j,Pi/p*k)]),i=0..n/2),j=0..n/2)] ,color=green),\n polygonp lot([seq(seq(op([triangleH1(2*i+1,2*j+1,Pi/p*k)]),i=0..n/2),j=0..n/2)] ,color=green),\n polygonplot([seq(seq(op([triangleH2(2*i,2*j, Pi/p*k)]),i=0..n/2),j=0..n/2)] ,color=yellow),\n polygonplot([ seq(seq(op([triangleH2(2*i+1,2*j-1,Pi/p*k)]),i=0..n/2),j=0..n/2)] ,col or=yellow)\n ],scaling=constrained,axes=none):\nend:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 985 "n:=3;\ndispo:=proc(p,k) global n:\n display([\n \+ polygonplot([seq(seq(op([diag1(2*i,2*j,Pi/p*k)]),i=0..n/2),j=0.. n/2)]), polygonplot([seq(seq(op([triangleV2(2*i,2*j, Pi/p*k)]),i=0..n/2),j=0..n/2)] ,color=blue),\n polygonplot([se q(seq(op([triangleV2(2*i+1,2*j+1,Pi/p*k)]),i=0..n/2),j=0..n/2)] ,color =blue),\n polygonplot([seq(seq(op([triangleV1(2*i,2*j,Pi/p*k)] ),i=0..n/2),j=0..n/2)] ,color=red),\n polygonplot([seq(seq(op( [triangleV1(2*i+1,2*j+1,Pi/p*k)]),i=0..n/2),j=0..n/2)] ,color=red),\n \n polygonplot([seq(seq(op([triangleH1(2*i,2*j,Pi/p*k)]),i=0.. n/2),j=0..n/2)] ,color=green),\n polygonplot([seq(seq(op([tria ngleH1(2*i+1,2*j+1,Pi/p*k)]),i=0..n/2),j=0..n/2)] ,color=green),\n \+ polygonplot([seq(seq(op([triangleH2(2*i,2*j,Pi/p*k)]),i=0..n/2),j =0..n/2)] ,color=yellow),\n polygonplot([seq(seq(op([triangleH 2(2*i+1,2*j-1,Pi/p*k)]),i=0..n/2),j=0..n/2)] ,color=yellow)\n ], scaling=constrained,axes=none):\nend:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 55 "p:=5;display([seq(dispo(p,k),k=2..2)],insequence=true);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG\"\"&" }}{PARA 13 "" 1 "" {GLPLOT2D 403 361 361 {PLOTDATA 2 "6#-%(ANIMATEG6#7--%)POLYGONSG637&7$$!+5N2g7! \"*$\"+F_R?k!#57$$!+F_R?kF1F,7$$\"+5N2g7F.F37$F/F67&7$$\"+Ul=iJF.F,7$$ \"+I0A!y$F.F/7$$\"+)\\2\"y=F.F6F57&F=7$$\"+=XD)R%F.F,7$$\"+]vO+jF.F37$ $\"+iNL#o&F.F67&7$$\"+#e![-#)F.F,7$$\"+qX^?))F.F/7$$\"+Q:S=pF.F6FG7&F8 7$F6F;7$F3F>7$F,FA7&FXF@7$F>FA7$F;F>7&FJ7$FHF;7$FEF>Ffn7&FinFT7$FRFA7$ FOF>7&7$F,FKFY7$F6FE7$F/FH7&Fgn7$F>FK7$FAFHF`o7&FcoFjn7$FHFE7$FKFH7&F] o7$FRFK7$FUFHFfo7&Fao7$F6FO7$F3FR7$F,FU7&F\\pFdo7$F>FU7$F;FR7&Fgo7$FHF O7$FEFRF`p7&FcpFjo7$FRFU7$FOFR-%'COLOURG6&%$RGBG$\"\"!F]q$\"*++++\"!\" )F^q-F(6'7%F@F5FX7%FTFGFin7%FdoF`oF\\p7%FjoFfoFcp-Fip6&F[qF\\qF\\qF^q- F(6'7%FjnFfnFco7%7$$\"+a&[&Q%*F.F>F\\oFio7%FdpF`p7$F>$\"+hFEs5F`q7%7$F ^rFRFfp7$FRFbrFgq-F(6'7%F5F8FX7%FGFJFin7%F`oFaoF\\p7%FfoFgoFcp-Fip6&F[ qF^qF\\qF\\q-F(6'7%FfnFgnFco7%F\\oF]oFio7%F`pFapFar7%FfpFgpFfrF]s-F(6' 7%F2F5F:7%FDFGFN7%FYF`oFgn7%FjnFfoF]o-Fip6&F[qF\\qF^qF\\q-F(6'7%F@FfnF J7%FTF\\o7$FbrF67%FdoF`pFgo7%FjoFfp7$FbrFHF[t-F(6'7%FXFYFgn7%FinFjnF]o 7%F\\pF]pFap7%FcpFdpFgp-Fip6&F[qF^qF^qF\\q-F(6'7%F=F@FJ7%FQFTFat7%FcoF doFgo7%FioFjoFdtF[u-%(SCALINGG6#%,CONSTRAINEDG-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Cur ve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Cur ve 9" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 21 " pentagones articul\351s" }}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 482 "aeq:= arcsin(( 1+sqrt(7))/4):\nevalf(2*aeq);#ou asin(sqrt(2)/4)+Pi/4:=arctan( (sqrt(7 )+1)/(sqrt(7)-1)) := 65.70\260 :=:=] cot\351s \351gaux - penta convex e ##3/4*pi-asin(sqrt(2)/4); # :=:=] cot\351s \351gaux - penta concave \+ # pi/4+0.001; # carr\351s# pi/3;:=:=] cot\351s non \351gaux #3*pi/ 4;# 2 triangles cote \340 cote # pi/2;# rectangle 2x1;\n p1:=(a) -> \+ [sin(a)-cos(a),0]: p2:=a -> [sin(a) , sin(a)]:\np3:=a -> [0, cos(a )+sin(a)]: p4:=a -> [-sin(a),sin(a)]: p5:= (a) -> [-sin(a)+cos(a), 0 ]: \n\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+u0`$H#!\"*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 92 "penta:=proc(a)\n \{[ p1(a),p2(a),p3(a),[0,0 ]],[[0,0],p3(a),p4(a),p5(a)]\}: \n end:\n" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 59 "penta:=proc(a)\n \{[ p1(a),p3(a),p5(a) ]\}: \n end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "polygo nplot(penta(Pi/3),color=cyan,scaling=constrained,axes=none);\n" }} {PARA 13 "" 1 "" {GLPLOT2D 300 345 345 {PLOTDATA 2 "6&-%)POLYGONSG6#7% 7$$\"+SSDgO!#5$\"\"!F,7$F+$\"+/a-m8!\"*7$$!+SSDgOF*F+-%'COLOURG6&%$RGB GF+$\"*++++\"!\")F8-%(SCALINGG6#%,CONSTRAINEDG-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 10 0 2 6 1 1 1 1.000000 47.000000 38.000000 0 0 "Curve 1" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 434 "\npentaSX:=proc(a) Ltrans(2 *p3(a)+perp(p1(a)-p5(a)) ,LsymX(penta(a))): end:\npentaY:=proc(a) Ltr ans(p1(a)+(p2(a)-p1(a))+p3(a)-(p1(a)+p5(a))/2+p4(a)-p3(a),LrotO(-Pi/2, penta(a))): end:\npentaSY:=proc(a) Ltrans(-perp(p4(a)-p2(a)) ,LrotO(Pi /2,penta(a))): end:\n#---- d\351placement en X -----\ndX:=a -> -perp(p 3(a))+p1(a): # +[r/2,0,0]: \n #---- d\351placement en Y ----- \n dY:=a ->( p3(a)+perp(p1(a)-p5(a))/2): # +[0,r/2,0]:\n\n#a:=Pi/3;penta(a); \n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "cdg:= proc(L) local \+ n; n:=nops(L): add(L[i],i=1..n)/n: end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2007 "p:=3;a:=Pi/3;\ngraphe:=proc(a)\n local gr,i,j: \n gr:=NULL:\n for i from 0 to p do:\n for j from 0 to p do:\n \+ gr:=gr,polygonplot( Ltrans((2*i)*dX(a)+2*j*dY(a),penta( a)),color=blue)\n# ,pointplot(map(cdg,Ltrans((2*i )*dX(a)+2*j*dY(a),penta(a))),color=white,symbol=circle,symbolsize=10) \n ,polygonplot( Ltrans((2*i)*dX(a)+(2*j+1)*dY(a )+dX(a),penta(a)),color=blue)\n #,pointplot(map(c dg,Ltrans((2*i)*dX(a)+(2*j+1)*dY(a)+dX(a),penta(a))),color=white,symbo l=circle,symbolsize=10)\n ,polygonplot( Ltrans(( 2*i)*dX(a)+2*j*dY(a),pentaSX(a)),color=red)\n# ,p ointplot(map(cdg,Ltrans((2*i)*dX(a)+2*j*dY(a),pentaSX(a))),color=white ,symbol=circle,symbolsize=10)\n ,polygonplot( Lt rans((2*i)*dX(a)+(2*j+1)*dY(a)+dX(a),pentaSX(a)),color=red)\n \+ #,pointplot(map(cdg,Ltrans((2*i)*dX(a)+(2*j+1)*dY(a)+dX(a ),pentaSX(a))),color=white,symbol=circle,symbolsize=10)\n \+ ,polygonplot( Ltrans((2*i)*dX(a)+2*j*dY(a),pentaSY(a)),color =yellow)\n# ,pointplot(map(cdg,Ltrans((2*i)*dX(a) +2*j*dY(a),pentaSY(a))),color=black,symbol=circle,symbolsize=10)\n \+ ,polygonplot( Ltrans((2*i)*dX(a)+(2*j+1)*dY(a)+dX(a ),pentaSY(a)),color=yellow)\n #,pointplot(map(cdg ,Ltrans((2*i)*dX(a)+(2*j+1)*dY(a)+dX(a),pentaSY(a))),color=black,symbo l=circle,symbolsize=10)\n ,polygonplot( Ltrans(( 2*i)*dX(a)+2*j*dY(a),pentaY(a)),color=green)\n# , pointplot(map(cdg, Ltrans((2*i)*dX(a)+2*j*dY(a),pentaY(a))),color=whit e,symbol=circle,symbolsize=10)\n ,polygonplot( L trans((2*i)*dX(a)+(2*j+1)*dY(a)+dX(a),pentaY(a)),color=green)\n \+ #,pointplot(map(cdg,Ltrans((2*i)*dX(a)+(2*j+1)*dY(a)+dX( a),pentaY(a))),color=white,symbol=circle,symbolsize=10) \+ :\n od:\n od:\n display([gr],style=patch,axes=none,scali ng=constrained);\nend:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG\"\"$ " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG,$*&\"\"$!\"\"%#PiG\"\"\"F* " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "graphe(aeq);" }}{PARA 13 "" 1 "" {GLPLOT2D 349 260 260 {PLOTDATA 2 "6_s-%)POLYGONSG6$7%7$$\" +,+++]!#5$\"\"!F,7$F+$\"+cc(GK\"!\"*7$$!+,+++]F*F+-%'COLOURG6&%$RGBGF+ F+$\"*++++\"!\")-F$6$7%7$$\"+bc(GK#F0$\"+cc(G#=F07$FA$\"+68vXJF07$F.FA 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"convert(2*sqrt(2)*sin(Pi/12),radical);evalf(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$\"\"$#\"\"\"\"\"#F'F'!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*330K(!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "A :=expand(tan(u)-cot(u-Pi/4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"A G,&-%$tanG6#%\"uG\"\"\"*&,&F*F*F&F*F*,&F*F*F&!\"\"F.F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "solve(A=1,u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%'arctanG6#\"\"$\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "2*evalf(arctan(3)*180/Pi);evalf((arctan(3)-Pi)*180/Pi );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+B5IJ9!\"(" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$!+)[\\V3\"!\"(" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 21 " rectangles articul\351s" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 390 "h:=0.4: #== rectangle de cot\351s 1 et h =======\nrect:=[[-h,-1 ],[h,-1],[h,1],[-h,1]]:\nt0:=arctan(1/h):\nrotrect:= t -> LrotO(t,rect ):\nrect_mobile:=proc(i,j,t)\n local tx,ty :\n tx:=2 *i*sqrt(1+h*h)*cos(t0-t): ty:=2*j*sqrt(1+h*h)*cos(Pi/2-t0-t):\n \+ Ltrans([tx,ty],rotrect( (2*((i+j) mod 2)-1)* t)):\nend:\n\nbaseV1:= t -> [op(rect_mobile(0,0,t)[3..4]),rect_mobile(0,1,t)[2]]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 950 "triangleV1:=proc(i,j,t) local tx,ty; \+ #------------- rouge ----------\n tx:=2*i*sqrt(1+h*h)*cos(t0-t ): ty:=2*j*sqrt(1+h*h)*cos(Pi/2-t0-t): \n Ltrans([tx,ty],baseV1(t)) :\nend:\nbaseV2:=t -> [op(rect_mobile(1,0,t)[3..4]),rect_mobile(1,1,t) [1]]:\ntriangleV2:=proc(i,j,t) local tx,ty; #------------- b leu ----------\n tx:=2*i*sqrt(1+h*h)*cos(t0-t): ty:=(2*j)*sqrt(1+h* h)*cos(Pi/2-t0-t):\n Ltrans([tx,ty],baseV2(t)):\nend:\n\nbaseH1:=t \+ -> [op(rect_mobile(0,0,t)[2..3]),rect_mobile(1,0,t)[1]]:\ntriangleH1:= proc(i,j,t) local tx,ty; #------------- vert ----------\n \+ tx:=2*i*sqrt(1+h*h)*cos(t0-t): ty:=(2*j)*sqrt(1+h*h)*cos(Pi/2-t0-t): \n Ltrans([tx,ty],baseH1(t)):\nend:\nbaseH2:=t -> [op(rect_mobile(0 ,1,t)[2..3]),rect_mobile(1,1,t)[4]]:\ntriangleH2:=proc(i,j,t) local tx ,ty; #------------- jaune ----------\n tx:=2*i*sqrt(1+h*h )*cos(t0-t): ty:=(2*j)*sqrt(1+h*h)*cos(Pi/2-t0-t):\n Ltrans([tx,ty] ,baseH2(t)):\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 972 "n:=3;\ndispo:=proc(p,k) gl obal n:\n display([polygonplot([seq(seq(rect_mobile(i,j,Pi/p*k),i=0..n +1),j=0..n+1)],color=cyan),\n polygonplot([seq(seq(op([triangl eV2(2*i,2*j,Pi/p*k)]),i=0..n/2),j=0..n/2)] ,color=blue),\n pol ygonplot([seq(seq(op([triangleV2(2*i+1,2*j+1,Pi/p*k)]),i=0..n/2),j=0.. n/2)] ,color=blue),\n polygonplot([seq(seq(op([triangleV1(2*i, 2*j,Pi/p*k)]),i=0..n/2),j=0..n/2)] ,color=red),\n polygonplot( [seq(seq(op([triangleV1(2*i+1,2*j+1,Pi/p*k)]),i=0..n/2),j=0..n/2)] ,co lor=red),\n\n polygonplot([seq(seq(op([triangleH1(2*i,2*j,Pi/p *k)]),i=0..n/2),j=0..n/2)] ,color=green)\n , polygonplot([seq(s eq(op([triangleH1(2*i+1,2*j+1,Pi/p*k)]),i=0..n/2),j=0..n/2)] ,color=gr een)\n ,polygonplot([seq(seq(op([triangleH2(2*i,2*j,Pi/p*k)]), i=0..n/2),j=0..n/2)] ,color=yellow)\n , polygonplot([seq(seq(op ([triangleH2(2*i+1,2*j-1,Pi/p*k)]),i=0..n/2),j=0..n/2)] ,color=yellow) \n ],scaling=constrained,axes=none):\nend:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "n:=2;p:=10;dispo(p,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\" \"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG\"#5" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 58 "p:=80;display([seq(dispo(p,k),k=0..p/2)],insequence=true);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG\"#!)" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 20 " Triangles articul\351s" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 871 "h:=0.5: #== rectangle de cot\351s 1 et h =======\ntri1:=[[0,0 ],[1,0],[0,h]]: tri2:=[[0,0],[1,0],[0,-h]]:\nrottri1:= t -> LrotO(t,t ri1): rottri2:= t -> LrotO(-t,tri2):\ndiag:=sqrt(1+h*h):\ntri1_mobile: =proc(i,j,t)\n local tx,ty :\n tx:=2*i*(cos(t)-h*cos (Pi/2+t)): ty:=(4*j)*h*sin(t):\n Ltrans([tx,ty],rottri1( t)) :\nend:\ntri2_mobile:=proc(i,j,t)\n local tx,ty :\n \+ tx:=(2*i+2)*(cos(t)-h*cos(Pi/2+t))+2*h*cos(Pi/2+t): ty:=(4*j)*h*sin(t) :\n Ltrans([tx,ty],rottri2( (t+Pi))): \nend:\ntri1X_mobile:=p roc(i,j,t)\n local tx,ty :\n tx:=2*i*(cos(t)-h*cos(P i/2+t)): ty:=(4*j)*h*sin(t):\n Ltrans([tx,ty],LsymX(rottri1(t ))):\nend:\ntri2X_mobile:=proc(i,j,t)\n local tx,ty :\n \+ tx:=(2*i+2)*(cos(t)-h*cos(Pi/2+t))+2*h*cos(Pi/2+t): ty:=(4*j)*h*si n(t):\n Ltrans([tx,ty],LsymX(rottri2( t+Pi) )): \nend:\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 492 "t0:=Pi/6;n:=2;\ngr:=proc(t0 )\n display([polygonplot(\{seq(seq(tri1_mobile(i,j,t0),i=0..n),j=0..n )\},color=cyan)\n ,polygonplot(\{seq(seq(tri2_mobile(i,j,t0),i =0..n),j=0..n)\},color=red)\n ,polygonplot(\{seq(seq(tri1X_mob ile(i,j,t0),i=0..n),j=0..n)\},color=yellow)\n ,polygonplot(\{s eq(seq(tri2X_mobile(i,j,t0),i=0..n),j=0..n)\},color=blue)\n \+ ],scaling=constrained);\nend:\ndep:=arctan(h);\np:=20;display([s eq(gr(dep+k/p*(Pi/2-dep)),k=0..p)],insequence=true,axes=none);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t0G,$*&\"\"'!\"\"%#PiG\"\"\"F*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$depG$\"+!4wkj%!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"pG\"#?" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "4 4 2 0" 2 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }