{VERSION 5 0 "IBM INTEL LINUX" "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 }{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 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 39 "Restart Map
le and clear any definitions" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "rest
art:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 25 "Load the p
lotting package" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 32 "Procedure for plot
ting a polygon" }}{PARA 0 "" 0 "" {TEXT -1 105 "   A polygon is a list
 of points [x,y]\n   In any procedure, nargs is the number of argument
s passed to it" }}{PARA 0 "" 0 "" {TEXT -1 41 "   args  is the list of
 arguments passed." }}{PARA 0 "" 0 "" {TEXT -1 64 "   So args[1] is th
e first argument, args[2] is the second etc.\n" }}{PARA 0 "" 0 "" 
{TEXT -1 60 "   A procedure can have any number of arguments passed to
 it" }}{PARA 0 "" 0 "" {TEXT -1 63 "   as long as we have at least as \+
many as are explicitly named." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 79 "   Below, if you pass a color as a second
 argument, the procedure can use it in" }}{PARA 0 "" 0 "" {TEXT -1 24 
"   the plotting command." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 129 "polyp
lot:=proc(poly)\n   if nargs > 1 then\n        polygonplot(poly,color=
args[2]):\n   else\n        polygonplot(poly)\n   end:\nend:" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 50 "Procedure for a reg
ular polygon with side length 1" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 258 
"regular1:=proc(n,theta)\n   local a, b, i, poly, r;\n   a:=2*Pi/n;\n \+
  b:=theta*Pi/180;\n   r:=1/(2*sin(a/2));\n   poly:=[[r*cos(b),r*sin(b
)]];\n   for i from 1 to n-1 do\n       b:=b+a;\n       poly:=[op(poly
), [r*cos(b),r*sin(b)]];\n   end:\n   RETURN(poly);\nend:   " }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 24 "The pieces of our t
iling" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "dodec:=regular1(12,15):" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "sqr:=regular1(4,45):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "hex:=regular1(6,30):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "polyplot(hex,green);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 57 "The distance betwee
n neighboring dodecagons in the tiling" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 16 "r:=1+cot(Pi/12):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "
evalf(r);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 52 "These
 are the translations that generate our tiling." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "T1:=x->[x[1],x[2]+r]:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "T2:=x->[x[1]+r*cos(Pi/6),x[2]+r*sin(Pi/6)]:" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 66 "This procedure appl
ies  all powers   T1^i T2^j   for i from 0 to n" }}{PARA 0 "" 0 "" 
{TEXT -1 42 "  and j from 0 to m   to the polygon poly." }}{PARA 0 "" 
0 "" {TEXT -1 82 "The color is clr.\nA second argument (in this case c
lr) can be passed in the  \"map\"" }}{PARA 0 "" 0 "" {TEXT -1 67 "comm
and by including it after the list of things to apply the given" }}
{PARA 0 "" 0 "" {TEXT -1 32 "command (in this case polyplot)." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 171 "tiles:=proc(n,m,T1,T2,poly,clr)\n \+
  map( polyplot, \n        [seq(   \n         seq( map( (T1@@i)@(T2@@j
) , poly ),\n         j=0..m),\n         i=0..n) ] ,\n         clr);\n
end:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 33 "Store a pl
ot in a named variable." }}{PARA 0 "" 0 "" {TEXT -1 72 "Be sure to put
 a : at the end so that all the raw data is not displayed." }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 40 "P1:=display(tiles(2,2,T1,T2,dodec,red)):" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 45 "Note thatt we hav
e to shift the square upward" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "P2:
=display(tiles(2,2,T1,T2,\n    map(x->[x[1],x[2]+r/2],sqr),blue)):" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 43 "Note that we shift
 the hexagon to the right" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "P3:=di
splay(tiles(2,2,T1,T2,\n    map(x->[x[1]+(cot(Pi/12)+cot(Pi/6))/2,x[2]
],hex),green)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "display(
\{P1,P2,P3\},axes=none,scaling=CONSTRAINED);" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }{TEXT -1 54 "Now we need more blue squares and more g
reen hexagons." }}{PARA 0 "" 0 "" {TEXT -1 34 "Then we will have the w
hole tiling" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 1 0" 
8 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }