{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 } 1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE " " -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 10 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 0 "" 0 "" {TEXT 256 39 "Construction of the marking of \+ a ruler" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 256 "> " 0 "" {MPLTEXT 1 0 82 "f:=proc(n) local k; global a; k:=n; while k>0 do k:=k-1;f(k);a:=[op(a),k]; od;end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"fG:6#%\"nG6#%\"kG6\"F*C$>8$9$?(F*\"\"\"F0F*2\"\"!F-C%>F-,&F-F0! \"\"F0-F$6#F->%\"aG7$-%#opG6#F:F-F*F>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "a:=[];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG7\"" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(6);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7[o\"\"!\"\"\"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$F%F$F'F$F%F$F&F$F%F$F(F$F%F$F &F$F%F$F'F$F%F$F&F$F%F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 " b:=array(1..63);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG-%&arrayG6$; \"\"\"\"#j7\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "for i to 6 3 do b[i]:=[[i,a[i]],[i,0]] od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 " plot(b,color=black);" }}{PARA 13 "" 1 "" {INLPLOT "6\\o-%'CURVESG6#7$7 $$\"\"\"\"\"!F*F'-F$6#7$7$$\"\"#F*F(7$F/F*-F$6#7$7$$\"\"$F*F*F5-F$6#7$ 7$$\"\"%F*F/7$FF*F*Fgr-F$6#7$7$$\"#?F*F/7$F^sF*-F$6#7$7$$\"#@F*F*Fds-F$6#7$7$$\" #AF*F(7$F[tF*-F$6#7$7$$\"#BF*F*Fat-F$6#7$7$$\"#CF*F67$FhtF*-F$6#7$7$$ \"#DF*F*F^u-F$6#7$7$$\"#EF*F(7$FeuF*-F$6#7$7$$\"#FF*F*F[v-F$6#7$7$$\"# GF*F/7$FbvF*-F$6#7$7$$\"#HF*F*Fhv-F$6#7$7$$\"#IF*F(7$F_wF*-F$6#7$7$$\" #JF*F*Few-F$6#7$7$$\"#KF*FC7$F\\xF*-F$6#7$7$$\"#LF*F*Fbx-F$6#7$7$$\"#M F*F(7$FixF*-F$6#7$7$$\"#NF*F*F_y-F$6#7$7$$\"#OF*F/7$FfyF*-F$6#7$7$$\"# PF*F*F\\z-F$6#7$7$$\"#QF*F(7$FczF*-F$6#7$7$$\"#RF*F*Fiz-F$6#7$7$$\"#SF *F67$F`[lF*-F$6#7$7$$\"#TF*F*Ff[l-F$6#7$7$$\"#UF*F(7$F]\\lF*-F$6#7$7$$ \"#VF*F*Fc\\l-F$6#7$7$$\"#WF*F/7$Fj\\lF*-F$6#7$7$$\"#XF*F*F`]l-F$6#7$7 $$\"#YF*F(7$Fg]lF*-F$6#7$7$$\"#ZF*F*F]^l-F$6#7$7$$\"#[F*F<7$Fd^lF*-F$6 #7$7$$\"#\\F*F*Fj^l-F$6#7$7$$\"#]F*F(7$Fa_lF*-F$6#7$7$$\"#^F*F*Fg_l-F$ 6#7$7$$\"#_F*F/7$F^`lF*-F$6#7$7$$\"#`F*F*Fd`l-F$6#7$7$$\"#aF*F(7$F[alF *-F$6#7$7$$\"#bF*F*Faal-F$6#7$7$$\"#cF*F67$FhalF*-F$6#7$7$$\"#dF*F*F^b l-F$6#7$7$$\"#eF*F(7$FeblF*-F$6#7$7$$\"#fF*F*F[cl-F$6#7$7$$\"#gF*F/7$F bclF*-F$6#7$7$$\"#hF*F*Fhcl-F$6#7$7$$\"#iF*F(7$F_dlF*-F$6#7$7$$\"#jF*F *Fedl-%'COLOURG6&%$RGBGF*F*F*" 2 299 299 299 2 0 1 0 2 6 0 4 2 1.000000 45.000000 45.000000 10030 10061 10056 10074 0 0 0 20030 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 180 3 0 0 0 0 0 1 }}}}{PARA 0 "" 0 "" {TEXT 257 39 "Construction of the Sierpinski Triangle" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 199 "s:=proc(n,a,b,c) local k,ma b,mbc,mca; global t; k:=n; while k>0 do k:=k-1;mab:=(a+b)/2; mbc:=(b+c )/2;mca:=(c+a)/2; s(k,a,mab,mca); s(k,b,mbc,mab); s(k,c,mbc,mca);t:=[o p(t),[mab,mbc,mca,mab]]; od;end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>% \"sG:6&%\"nG%\"aG%\"bG%\"cG6&%\"kG%$mabG%$mbcG%$mcaG6\"F0C$>8$9$?(F0\" \"\"F6F02\"\"!F3C*>F3,&F3F6!\"\"F6>8%,&9%#F6\"\"#9&FA>8&,&FCFA9'FA>8', &FGFAF@FA-F$6&F3F@F>FI-F$6&F3FCFEF>-F$6&F3FGFEFI>%\"tG7$-%#opG6#FR7&F> FEFIF>F0FV" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "t:=[];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tG7\"" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 23 "s(5,[0,1],[1,0],[0,0]):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 30 "plot(t,color=black,axes=none);" }}{PARA 13 "" 1 "" {INLPLOT "6c`l-%'CURVESG6#7&7$$\"1++++++DJ!#<$\"1+++++](o*!#;7$F($\"1+ +++++v$*F-7$\"\"!F+F'-F$6#7&7$$F0F*$\"1++++++]()F-7$$\"1++++++]iF*$\"1 +++++]i!*F-7$F7F=F6-F$6#7&7$F(F87$F(F=7$F2F=FC-F$6#7&7$F;F/7$F;F87$F2F /FIFF-F$6#7&7$$\"1+++++](=#F-$\"1+++++++vF-7$$\"1++++++v=F-$\"1+++++]7 yF-7$FPFWFO-F$6#7&7$$\"1++++++]7F-FW7$$\"1+++++]i:F-FW7$F[oFRFgn-F$6#7 &7$Fhn$\"1+++++]P%)F-7$F[o$\"1++++++D\")F-7$F[oFboFao-F$6#7&7$FUFR7$Fh nFeo7$FUFeoF[pFho-F$6#7&7$F(FR7$F(FW7$F2FWFap-F$6#7&7$F7FW7$F;FW7$F7FR Fgp-F$6#7&7$F(Fbo7$F(Feo7$F2FboF]q-F$6#7&7$F;FR7$F;Feo7$F2FeoFcqF`q-F$ 6#7&7$FhnF87$FhnFR7$F2F8FiqFFFhoF`qFfqFfq-F$6#7&7$$\"1+++++](o%F-$\"1+ ++++++]F-7$$\"1++++++vVF-$\"1+++++]7`F-7$F`rFgrF_r-F$6#7&7$$\"1++++++] PF-Fgr7$$\"1+++++]iSF-Fgr7$FasFbrF]s-F$6#7&7$F^s$\"1+++++]PfF-7$Fas$\" 1++++++DcF-7$FasFhsFgs-F$6#7&7$FerFbr7$F^sF[t7$FerF[tFatF^t-F$6#7&7$$ \"1+++++++DF-Fgr7$$\"1+++++]7GF-Fgr7$F[uFbrFgt-F$6#7&7$F[uFhs7$F[uF[t7 $FhtFhsFau-F$6#7&7$$\"1+++++]PMF-Fgr7$$F)F-Fgr7$FhuFbrFgu-F$6#7&7$FhtF [t7$F[vF[t7$F[vFbrF`vF]v-F$6#7&7$Fht$\"1+++++](=(F-7$F[u$\"1++++++voF- 7$F[uFgvFfv-F$6#7&7$F[u$F " 0 "" {MPLTEXT 1 0 356 "snow:=proc(n,lx,ly,rx,ry) local mlx, mly, \+ mrx, mry, kx, ky; mlx:=(2*lx+rx)/3;mly:=(2*ly+ry)/3;mrx:=(lx+2*rx)/3;m ry:=(ly+2*ry)/3;kx:=(mlx+mrx)/2+3^(1/2)*(mly-mry)/2;ky:=(mly+mry)/2+3^ (1/2)*(mrx-mlx)/2;if n=0 then [[lx,ly],[rx,ry]] else [op(snow(n-1,lx,l y,mlx,mly)),op(snow(n-1,mlx,mly,kx,ky)),op(snow(n-1,kx,ky,mrx,mry)),op (snow(n-1,mrx,mry,rx,ry))] fi end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6# >%%snowG:6'%\"nG%#lxG%#lyG%#rxG%#ryG6(%$mlxG%$mlyG%$mrxG%$mryG%#kxG%#k yG6\"F3C)>8$,&9%#\"\"#\"\"$9'#\"\"\"F;>8%,&9&F99(F=>8&,&F8F=F8',&F BF=FCF9>8(,(F6#F>F:FEFM*&F;FM,&F@F>FH!\"\"F>FM>8),(F@FMFHFM*&F;FM,&FEF >F6FPF>FM@%/9$\"\"!7$7$F8FB7$FFPF>F8FBF6F@-Fin 6#-F$6'F]oF6F@FKFR-Fin6#-F$6'F]oFKFRFEFH-Fin6#-F$6'F]oFEFHF " 0 "" {MPLTEXT 1 0 5 "j:=2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"jG\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "a:=snow(j,cos(2*Pi/3),sin(2*Pi/3),1,0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "b:=snow(j,1,0,cos(2*Pi/3),-sin(2*Pi/3)):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "c:=snow(j,cos(2*Pi/3),-sin(2 *Pi/3),cos(2*Pi/3),sin(2*Pi/3)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "plot([op(a),op(b),op(c)],color=black,axes=none);" }} {PARA 13 "" 1 "" {INLPLOT "6%-%'CURVESG6#7\\q7$$!1+++++++]!#;$\"1'QWy. a-m)F*7$$!1LLLLLLLLF*$\"14]>*e.!)p(F*F-7$$!1nmmmmmm;F*F+F27$F3$\"1McaS JvNnF*F57$\"\"!$\"1di*=p-Nx&F*F87$$\"1nmmmmmm;F*F6F<7$F=F+F?7$$\"1LLLL LLLLF*F0F@7$$\"1+++++++]F*F+FC7$FDF6FF7$$\"1mmmmmmmmF*F:FG7$FD$\"1\")o CVAD6[F*FJ7$FD$\"1H\"[fM^n)GF*FM7$FH$\"1_()H(*3]C>F*FP7$$\"1MLLLLLL$)F *FNFS7$FT$\"1iP\\'[/Di*!#F*F]o7$FDF[oF`o7$FD$!1\")oCVAD6[F*Fa o7$FH$!1di*=p-Nx&F*Fdo7$FD$!1McaSJvNnF*Fgo7$FD$!1'QWy.a-m)F*Fjo7$FA$!1 4]>*e.!)p(F*F]p7$F=F[pF`p7$F=FhoFap7$F9FeoFbp7$F3FhoFcp7$F3F[pFdp7$F.F ^pFep7$F(F[pFfp7$F(FhoFgp7$$!1mmmmmmmmF*FeoFhp7$F(FboF[q7$F(F[oF\\q7$F ipF^oF]q7$$!1MLLLLLL$)F*F[oF^q7$F_qFhnFaq7$$!\"\"F9F9Fbq7$F_qFWFeq7$F_ qFNFfq7$FipFQFgq7$F(FNFhq7$F(FKFiq7$FipF:Fjq7$F(F6F[rF'-%*AXESSTYLEG6# %%NONEG-%'COLOURG6&%$RGBGF9F9F9" 2 299 299 299 2 0 1 0 2 6 0 1 1 1.000000 45.000000 45.000000 10030 10061 10056 10074 0 0 0 20040 0 12010 0 0 0 0 0 0 0 1 0 0 0 0 0 37 0 0 0 0 0 1 }}}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "5 1 1 0" 0 }{VIEWOPTS 1 0 0 1 1 1803 }