{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 "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 0 "" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "sommet:=k->[cos(k*Pi/n),sin( k*Pi/n),(-1)^(k+1)*a]:S:=[0,0,b]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "face:=k->[sommet(k-1),sommet(k),sommet(k+1),[0,0,(-1) ^k*b]]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "b:=-1/(3-4*sin(1 /2*Pi/n)^2)^(1/2)*(sin(1/2*Pi/n)+1)*(sin(1/2*Pi/n)-1)/sin(1/2*Pi/n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG,$**,&\"\"$\"\"\"*&\"\"%F))-%$ sinG6#,$*(\"\"#!\"\"%#PiGF)%\"nGF3F)F2F)F3#F3F2,&F-F)F)F)F),&F-F)F)F3F )F-F3F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "a:=b*tan(Pi/2/n) ^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG*&%\"bG\"\"\")-%$tanG6#,$ *(\"\"#!\"\"%#PiGF'%\"nGF/F'F.F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "b:=1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "n:= 5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 132 "rec:=display(seq(pol ygonplot3d(face(2*i)),i=1..n),seq(polygonplot3d(face(2*i+1)),i=1..n),l ightmodel=light3,scaling=constrained):rec;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 13 "" 1 "" {GLPLOT3D 496 496 496 {PLOTDATA 3 "6.-%)POLYGONSG6#7&7%$\"+V*p,4)!#5$\"+CD&y(eF*$\"+!4Gd0\"F*7%$\"+Q*p ,4$F*$\"+l^c5&*F*$!+!4Gd0\"F*7%$!+Q*p,4$F*F2F-7%$\"\"!F;F:$\"\"\"F;-F$ 6#7&F67%$!+V*p,4)F*F+F47%$!\"\"F;F:F-F9-F$6#7&FD7%FB$!+CD&y(eF*F47%F7$ !+l^c5&*F*F-F9-F$6#7&FM7%F0FNF47%F(FKF-F9-F$6#7&FT7%F " 0 "" {MPLTEXT 1 0 42 "scal:=proc(X,Y) \nsum(X[k]*Y[k],k=1..3)\nend;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sc alGf*6$%\"XG%\"YG6\"F)F)-%$sumG6$*&&9$6#%\"kG\"\"\"&9%F0F2/F1;F2\"\"$F )F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "d:=(X,Y)->expand(X -Y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "A:=scal(d(sommet(- 1),sommet(0)),d(sommet(1),sommet(0)))^2/scal(d(sommet(-1),sommet(0)),d (sommet(-1),sommet(0)))/scal(d(sommet(1),sommet(0)),d(sommet(1),sommet (0))); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG*&,(*$),&\"\"\"!\"\"- %$cosG6#*&%#PiGF*%\"nGF+F*\"\"#F*F**$)-%$sinGF.F2F*F+*(\"\"%F*)%\"bGF2 F*)-%$tanG6#,$*(F2F+F0F*F1F+F*F8F*F*F2,(F'F*F3F**(F8F*F9F*F;F*F*!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 138 "B:=scal(d(sommet(1),S),d (sommet(1),sommet(0)))^2/scal(d(sommet(1),S),d(sommet(1),S))/scal(d(so mmet(1),sommet(0)),d(sommet(1),sommet(0))); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG*(,(*&-%$cosG6#*&%#PiG\"\"\"%\"nG!\"\"F-,&F-F/F(F -F-F-*$)-%$sinGF*\"\"#F-F-**F5F-,&%\"bGF/*&F8F-)-%$tanG6#,$*(F5F/F,F-F .F/F-F5F-F-F-F8F-F:F-F-F5,(*$)F(F5F-F-F1F-*$)F7F5F-F-F/,(*$)F0F5F-F-F1 F-*(\"\"%F-)F8F5F-)F;FIF-F-F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "solve(A=B,b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&*(,&-%$sinG6#,$ *(\"\"#!\"\"%#PiG\"\"\"%\"nGF+F-F-F-F-F-,&F%F-F-F+F-^#F-F-*(^#F+F-F$F- F/F-,$**,&\"\"$F-*&\"\"%F-)F%F*F-F+#F+F*F$F-F/F-F%F+F+F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "1/(3-4*sin(1/2*Pi/n)^2)^(1/2)*(sin( 1/2*Pi/n)+1)*(sin(1/2*Pi/n)-1)/sin(1/2*Pi/n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**,&\"\"$\"\"\"*&\"\"%F&)-%$sinG6#,$*(\"\"#!\"\"%#PiGF& %\"nGF0F&F/F&F0#F0F/,&F*F&F&F&F&,&F*F&F&F0F&F*F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "b:=1/(3-4*sin(1/2*Pi/n)^2)^(1/2)*(sin(1/2*Pi/ n)+1)*(sin(1/2*Pi/n)-1)/sin(1/2*Pi/n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG**,&\"\"$\"\"\"*&\"\"%F()-%$sinG6#,$*(\"\"#!\"\"%#PiGF(%\" nGF2F(F1F(F2#F2F1,&F,F(F(F(F(,&F,F(F(F2F(F,F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 449 "n :=5:d:=2:faces:=[seq(\n[[cos(2*k*d*Pi/n),sin(2*k*d*Pi/n),1/2],\n[cos(2 *(k+1/2)*d*Pi/n),sin(2*(k+1/2)*d*Pi/n),-1/2]\n,[cos(2*(k+1)*d*Pi/n),si n(2*(k+1)*d*Pi/n),1/2],\n[0,0,1],\n[cos(2*k*d*Pi/n),sin(2*k*d*Pi/n),1/ 2]],\nk=0..n-1),seq(\n[[cos(2*(k-1/2)*d*Pi/n),sin(2*(k-1/2)*d*Pi/n),-1 /2],\n[cos(2*(k)*d*Pi/n),sin(2*(k)*d*Pi/n),1/2]\n,[cos(2*(k+1/2)*d*Pi/ n),sin(2*(k+1/2)*d*Pi/n),-1/2],\n[0,0,-1],\n[cos(2*(k-1/2)*d*Pi/n),sin (2*(k-1/2)*d*Pi/n),-1/2]],\nk=0..n-1)]:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "display(polygonplot3d(faces),lightmodel=light3,scalin g=constrained);" }}{PARA 13 "" 1 "" {GLPLOT3D 913 522 522 {PLOTDATA 3 "6%-%)POLYGONSG6,7'7%$\"\"\"\"\"!$F*F*$\"+++++]!#57%$\"+Q*p,4$F.$\"+l^ c5&*F.$!+++++]F.7%$!+V*p,4)F.$\"+CD&y(eF.F,7%F+F+F(F'7'F67%F7$!+CD&y(e F.F47%F0$!+l^c5&*F.F,F;F67'F@7%F(F+F47%F0F2F,F;F@7'FE7%F7F9F47%F7F>F,F ;FE7'FH7%F0FAF4F'F;FH7'FJF'F/7%F+F+$!\"\"F*FJ7'F/F6F=FLF/7'F=F@FDFLF=7 'FDFEFGFLFD7'FGFHFJFLFG-%+LIGHTMODELG6#%(LIGHT_3G-%(SCALINGG6#%,CONSTR AINEDG" 1 2 0 1 10 0 2 1 5 1 1 1.000000 87.000000 87.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 430 "n:=5:d:=2:faces:=[s eq(\n[[cos(2*k*d*Pi/n),sin(2*k*d*Pi/n),1/2],\n[cos(2*(k+1/2)*d*Pi/n),s in(2*(k+1/2)*d*Pi/n),-1/2]\n,[cos(2*(k+1)*d*Pi/n),sin(2*(k+1)*d*Pi/n), 1/2],\n[cos(2*k*d*Pi/n),sin(2*k*d*Pi/n),1/2]],\nk=0..n-1),seq(\n[[cos( 2*(k-1/2)*d*Pi/n),sin(2*(k-1/2)*d*Pi/n),-1/2],\n[cos(2*(k)*d*Pi/n),sin (2*(k)*d*Pi/n),1/2]\n,[cos(2*(k+1/2)*d*Pi/n),sin(2*(k+1/2)*d*Pi/n),-1/ 2],\n[cos(2*(k-1/2)*d*Pi/n),sin(2*(k-1/2)*d*Pi/n),-1/2]],\nk=0..n-1)]: \n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "display(polygonplot3d(faces), lightmodel=light3,scaling=constrained);" }}{PARA 13 "" 1 "" {GLPLOT3D 541 506 506 {PLOTDATA 3 "6%-%)POLYGONSG6,7&7%$\"\"\"\"\"!$F*F*$\"+++++ ]!#57%$\"+Q*p,4$F.$\"+l^c5&*F.$!+++++]F.7%$!+V*p,4)F.$\"+CD&y(eF.F,F'7 &F67%F7$!+CD&y(eF.F47%F0$!+l^c5&*F.F,F67&F?7%F(F+F47%F0F2F,F?7&FD7%F7F 9F47%F7F=F,FD7&FG7%F0F@F4F'FG7&FIF'F/FI7&F/F6F " 0 "" {MPLTEXT 1 0 40 "ps:=proc(X,Y)\nsum(X[k]*Y[k],k=1..3)\nend;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#psGf*6$%\"XG%\"YG6\"F)F)-%$sumG6$* &&9$6#%\"kG\"\"\"&9%F0F2/F1;F2\"\"$F)F)F)" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 73 "pv:=(U,V)->[U[2]*V[3]-U[3]*V[2],U[3]*V[1]-U[1]*V[3] ,U[1]*V[2]-U[2]*V[1]]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "s ommet:=k->[cos(k*Pi/n),sin(k*Pi/n),(-1)^(k+1)*a];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'sommetGf*6#%\"kG6\"6$%)operatorG%&arrowGF(7%-%$cosG6 #*(9$\"\"\"%#PiGF2%\"nG!\"\"-%$sinGF/*&)F5,&F1F2F2F2F2%\"aGF2F(F(F(" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "a:=sqrt(sin(Pi/2/n)*sin(3* Pi/2/n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG*$*&-%$sinG6#,$*(\" \"#!\"\"%#PiG\"\"\"%\"nGF-F/F/-F(6#,$**\"\"$F/F,F-F.F/F0F-F/F/#F/F," } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "U:=sommet(0)-sommet(1);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UG7%,&-%$cosG6#*&%#PiG\"\"\"%\"nG !\"\"F.F,F,,$-%$sinGF)F.,$*&\"\"#F,*&-F16#,$*(F4F.F+F,F-F.F,F,-F16#,$* *\"\"$F,F4F.F+F,F-F.F,F,#F,F4F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "V:=sommet(1)-sommet(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"VG7%,&-%$cosG6#,$*(\"\"#\"\"\"%#PiGF-%\"nG!\"\"F-F0-F(6#*&F.F-F/F0F- ,&-%$sinGF)F0-F6F2F-,$*&F,F-*&-F66#,$*(F,F0F.F-F/F0F-F--F66#,$**\"\"$F -F,F0F.F-F/F0F-F-#F-F,F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "W:=sommet(2)-sommet(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"WG7%,& -%$cosG6#,$*(\"\"$\"\"\"%#PiGF-%\"nG!\"\"F-F0-F(6#,$*(\"\"#F-F.F-F/F0F -F-,&-%$sinGF)F0-F8F2F-,$*&F5F-*&-F86#,$*(F5F0F.F-F/F0F-F--F86#,$**F,F -F5F0F.F-F/F0F-F-#F-F5F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "H:=pv(U,V);K:=pv(V,W);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"HG7%,&* (\"\"#\"\"\"-%$sinG6#*&%#PiGF)%\"nG!\"\"F)*&-F+6#,$*(F(F0F.F)F/F0F)F)- F+6#,$**\"\"$F)F(F0F.F)F/F0F)F)#F)F(F0*(F(F)F1F;,&-F+6#,$*(F(F)F.F)F/F 0F)F0F*F)F)F),&*(F(F)F1F;,&-%$cosGF?F0-FFF,F)F)F0*(F(F),&FGF0F)F)F)F1F ;F0,&*&FIF)F=F)F)*&F*F)FDF)F)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"K G7%,&*(\"\"#\"\"\"*&-%$sinG6#,$*(F(!\"\"%#PiGF)%\"nGF0F)F)-F,6#,$**\" \"$F)F(F0F1F)F2F0F)F)#F)F(,&-F,6#,$*(F(F)F1F)F2F0F)F0-F,6#*&F1F)F2F0F) F)F0*(F(F)F*F8,&-F,6#,$*(F7F)F1F)F2F0F)F0F:F)F)F0,&*(F(F)F*F8,&-%$cosG FDF0-FKF;F)F)F)*(F(F)F*F8,&FLF0-FKF?F)F)F),&*&FNF)FBF)F)*&F9F)FIF)F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "angle:=simplify(combine(p s(H,K)/sqrt(ps(H,H)*ps(K,K))));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%& angleG,$*&#\"\"#\"\"$\"\"\"*&,.*&\"\"%F*-%$cosG6#*&%#PiGF*%\"nG!\"\"F* F*F)F5*&F.F*-F06#,$*(F(F*F3F*F4F5F*F*F**&\"\"'F*-F06#,$*(F)F*F3F*F4F5F *F*F5-F06#,$*(F.F*F3F*F4F5F*F5*&F(F*-F06#,$*(\"\"&F*F3F*F4F5F*F*F*F*,, *&\"#cF*FAF*F*\"#qF**&\"$7\"F*F7F*F5*&\"#;F*-F06#,$*(F \+ " 0 "" {MPLTEXT 1 0 40 "seq(evalf(arccos(angle)*180/Pi),n=3..6);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6&$\"+2Ar%4\"!\"($\"+Hg^v7F%$\"+Vo*=Q\"F %$\"+9*=AX\"F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "limit(arc cos(angle),n=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#PiG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "eval(subs(n=6,angle));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(\"\"#\"\"\"\"\"$!\"\"F'#F&F%F(#F&F 'F&" }}}{EXCHG {PARA 0 "" 0 "" {GLPLOT3D 340 406 406 {PLOTDATA 3 "69-% )POLYGONSG6#7%7%$\"\"!F)F($\"\"$F)7%$!\"\"F)$\"+330KFDFL- F$6#7%FOF,FA-F$6#7%FAF4FG-F$6#7%FGF:FO-F$6#7%FO7%F-F/$!\"#F)FA-F$6#7%F A7%F-F5FinFG-F$6#7%FG7%F2F(FinFO-F$6#7%FhnFAF^o-F$6#7%F^oFGFbo-F$6#7%F boFOFhn-F$6#7%7%F(F(FBFhnF^o-F$6#7%F_pF^oFbo-F$6#7%F_pFboFhn-%(SCALING G6#%,CONSTRAINEDG-%+LIGHTMODELG6#%(LIGHT_3G" 1 2 0 1 10 0 2 1 1 1 1 1.000000 94.000000 116.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curv e 11" "Curve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17 " "Curve 18" "Curve 19" "Curve 20" "Curve 21" }}{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 22 "a1:=5:a2:=3:b:=4:c:=5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "sommet2:=(k,l)->[b*cos(2*k*Pi/n),b*sin(2*k*Pi /n),(-1)^(l)*a2]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "sommet 1:=k->[c*cos((2*k+1)*Pi/n),c*sin((2*k+1)*Pi/n),0]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "face1:=k->[[0,0,a1],sommet2(k,0),sommet2(k+ 1,0)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "face2:=k->[sommet 2(k,0),sommet1(k),sommet2(k+1,0)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "face3:=k->[sommet2(k,0),sommet1(k),sommet2(k+1,0)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "face4:=k->[sommet1(k-1),s ommet2(k,0),sommet1(k)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "face5:=k->[sommet1(k-1),sommet2(k,1),sommet1(k)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "face6:=k->[sommet2(k,1),sommet1(k),sommet2( k+1,1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "face7:=k->[[0,0 ,-a1],sommet2(k,1),sommet2(k+1,1)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 311 "n:=10:display(seq(polygonplot3d(face1(i)),i=1..n),\n seq(polygonplot3d(face2(i)),i=1..n),\nseq(polygonplot3d(face3(i)),i=1. .n),\nseq(polygonplot3d(face4(i)),i=1..n),\nseq(polygonplot3d(face5(i) ),i=1..n),\nseq(polygonplot3d(face6(i)),i=1..n),\nseq(polygonplot3d(fa ce7(i)),i=1..n),lightmodel=light3,scaling=constrained);" }}{PARA 13 " " 1 "" {GLPLOT3D 407 462 462 {PLOTDATA 3 "6do-%)POLYGONSG6#7%7%$\"\"!F )F($\"\"&F)7%$\"+xz1OK!\"*$\"+559^BF/$\"\"$F)7%$\"+vz1O7F/$\"+mgA/QF/F 2-F$6#7%F'F47%$!+vz1O7F/F7F2-F$6#7%F'F<7%$!+xz1OKF/F0F2-F$6#7%F'FB7%$! 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