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oolbook" 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 
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nt 3" -1 258 1 {CSTYLE "" -1 -1 "Helvetica" 1 24 0 0 0 0 2 1 2 0 0 0 
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-1 -1 "Helvetica" 1 24 0 0 0 0 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 
0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 6" -1 261 1 {CSTYLE "" -1 -1 "Helveti
ca" 1 24 0 0 0 0 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 
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-1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "normal" -1 264 1 {CSTYLE "" -1 -1 "ne
w century schoolbook" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 
-1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 4 265 1 {CSTYLE "" -1 -1 "new century \+
schoolbook" 1 18 255 0 0 1 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 
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{SECT 0 {PARA 263 "" 0 "" {TEXT 256 59 "MAPLE WORKSHEET #1: 2d Polygon
plots and Graphic Primitives." }}{SECT 1 {PARA 3 "" 0 "" {TEXT 258 23 
"Load the plots package:" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning,
 the name changecoords has been redefined\n" }}}}{SECT 1 {PARA 3 "" 0 
"" {TEXT 257 50 "Define the vertices of a  regular n-sided polygon:" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "ngon:=(a,b,r,n)-> \n[seq(\n
[a+r*cos(2*Pi*k/n),b+r*sin(2*Pi*k/n)],k = 0..n-1\n) \n]:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "ngon0:=n->ngon(0,0,1,n):" }}}{PARA 
0 "" 0 "" {TEXT -1 14 "Four octagons:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 106 "polygonplot(\{\nngon(1,0,1,8),ngon(0,1,1,8),ngon(-1,
0,1,8),ngon(0,-1,1,8)\n\},\nscaling=constrained,axes=none);" }}}}
{SECT 1 {PARA 3 "" 0 "" {TEXT -1 46 "Plot a pentagon with various opti
ons/settings:" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 39 "Plot the pentago
n with various options:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "p
olygonplot(ngon0(5),\naxes=none, color=cyan, scaling=constrained);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "polygonplot(ngon0(5),\naxe
s=none, color=cyan, scaling=constrained,\ntitlefont=[HELVETICA,BOLD,24
], title=`Pentagon`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 138 "p
ent := polygonplot(ngon0(5),\naxes=none, color=cyan, scaling=constrain
ed,\ntitlefont=[HELVETICA,BOLD,24], title=`Pentagon`):\ndisplay(pent);
" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Add text:" }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 90 "tex := textplot([0,0,`Inside a Pentagon`],
\nfont=[TIMES,ROMAN,38], color=COLOR(RGB,1,1,0)):" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 20 "display(\{pent,tex\});" }}}}{SECT 1 {PARA 4 
"" 0 "" {TEXT -1 13 "Add boundary:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 135 "wirepent := polygonplot(ngon0(5),\naxes=none, color=
red, scaling=constrained, \nstyle=line, thickness=5, linestyle=2):\ndi
splay(wirepent);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "display
(\{ pent, wirepent, tex\});" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 259 
57 "Create a figure for the proof of the Pythagorean Theorem:" }}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 26 "First create the polygons:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 158 "pyt1 := polygonplot(\n[ [0,
0],[1,2],[3,3],[3,0],[1,0],[1,3],[0,3],\n[0,2],[3,2],[3,3],[1,3],[1,0]
,[0,0],[0,2] ],\nstyle=line, thickness=3, color=red, axes=none):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "pyt2 := polygonplot(\n[ [4,
0],[7,0],[7,3],[4,3],[4,0],[5,0],[7,1],[6,3],[4,2],[5,0] ],\nstyle=lin
e, thickness=3, color=red, axes=none):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 85 "pyt3 := polygonplot(\n[ [1,0],[3,0],[3,2],[1,2],[1,0]
 ],\ncolor=aquamarine, axes=none):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 85 "pyt4 := polygonplot(\n[ [0,2],[1,2],[1,3],[0,3],[0,2]
 ],\ncolor=aquamarine, axes=none):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 86 "pyt5 := polygonplot(\n[ [5,0],[7,1],[6,3],[4,2],[5,0]
 ], \ncolor=aquamarine, axes=none):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 138 "pyt6 := textplot(\n\{[0.5,-0.15,`a`],[4.5,-0.15,`a`]
,[2,-0.15,`b`],[6,-0.15,`b`],\n[0.53,0.79,`c`],[4.47,0.73,`c`]\},\nfon
t=[COURIER,BOLD,18]):" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 33 "Then  \+
display all these together:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
137 "display(\{pyt1,pyt2,pyt3,pyt4,pyt5,pyt6\},\nscaling=constrained, \+
\ntitlefont=[HELVETICA,BOLD,24], \ntitle=`Proof of the Pythagorean The
orem`);" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 44 "A figure for determ
ining the golden section:" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 29 "The \+
vertices of the pentagon:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 
"P:=n->[sin(2*Pi*n/5),cos(2*Pi*n/5)]:" }}}}{SECT 1 {PARA 4 "" 0 "" 
{TEXT -1 69 "The line segments P(1)P(3) and P(2)P(4) intersect on the \+
y-axis at Q:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "slope:=(P(1)
[2]-P(3)[2])/(P(1)[1]-P(3)[1]):\nQ:=[0,P(1)[2]-slope*P(1)[1]]:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "penta := polygonplot([seq(P(
n), n=0..4)],\ncolor=red, thickness=4):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 63 "r1 := polygonplot([[P(1),Q],[P(4),Q]],\ncolor=red, th
ickness=4):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "r2 := polygo
nplot([P(1),P(4)],\ncolor=gold, thickness=4):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 64 "r3 := polygonplot([[P(2),Q],[P(3),Q]],\ncolor=bl
ue, thickness=4):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 178 "label
s := textplot(\{ \n[0.5298,0.7311,`1`],[-0.004567,0.3876,`golden secti
on=g`],\n[-0.4439,-0.1386,`1`],[0.3764,-0.5394,`1/g`], [-0.02436,-0.90
176,`1`] \n\},\nfont=[TIMES,ROMAN,22]):" }}}}{SECT 1 {PARA 4 "" 0 "" 
{TEXT -1 27 "Display all these together:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 112 "display(\{penta, r1, r2, r3, labels\},\nstyle=line, \+
axes=none, scaling=constrained,\ntitlefont=[HELVETICA,BOLD,22]);" }}}}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 26 "Add two similar triangles:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "r4:=polygonplot([[P(1),Q,P(4
)],[P(2),P(3),Q]],\nstyle=patch,color=cyan):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 132 "display(\{penta, r1, r2, r3, r4, labels\},\nsty
le=line, axes=none, scaling=constrained,\ntitlefont=[HELVETICA,BOLD,24
],title=`1+1/g=g`);" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 53 "Plot th
e 96-sided regular polygon with symmetry axes:" }}{SECT 1 {PARA 4 "" 
0 "" {TEXT -1 19 "First the polygon:\003" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 132 "polygonplot(ngon0(96),\naxes=none, color=red, scalin
g=constrained,\ntitlefont=[HELVETICA,BOLD,24],title=`A 96-sided regula
r polygon`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "plot([cos(
u), sin(u), u=0..2*Pi],\nnumpoints=250, thickness=2, scaling=constrain
ed, \ncolor=blue, tickmarks=[0,0]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 209 "display(\n\{ polygonplot(ngon0(96), color=red), \npl
ot([cos(u), sin(u), u=0..2*Pi], color=blue, numpoints=500, thickness=2
) \},\nview=[0.7039..0.7124,0.7034..0.7109], thickness=2, \naxes=none,
 scaling=constrained );" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 14 "Then
 the axes:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 153 "symmax := (k,
l)->polygonplot([ \n[1.2*cos(2*k*Pi/l),1.2*sin(2*k*Pi/l)], \n[-1.2*cos
(2*k*Pi/l),-1.2*sin(2*k*Pi/l)] \n],\nthickness=2, style=line, color=bl
ue):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 186 "display(\{ \npolyg
onplot(ngon0(5), style=patch, color=red),\nseq(symmax(k,5), k=0..4) \n
\},\naxes=none, scaling=constrained,\ntitlefont=[HELVETICA,BOLD,24], t
itle=`Symmety axes of a pentagon`);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 188 "display(\{ \npolygonplot(ngon0(96), style=patch, col
or=red),\nseq(symmax(k,96), k=0..95) \n\},\naxes=none, scaling=constra
ined,\ntitlefont=[HELVETICA,BOLD,24], title=`Symmetry axes of a 96-gon
`);" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 17 "Hexagonal tiling:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "hex := (a,b,c1,c2,c3)->polyg
onplot( \nngon(a,b,1,6),\ncolor=COLOR(RGB,c1,c2,c3)):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 188 "display(\{ \nhex(0,0,1,0,0),\nseq(
 \nhex(sqrt(3)*cos(Pi/6+2*k*Pi/6), sqrt(3)*sin(Pi/6+2*k*Pi/6), \nevalf
(sin(k/4)),evalf(cos(k/4)),evalf(sin(k/4))), \nk=1..6) \n\},\naxes=non
e,scaling=constrained);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 51 " Pie
chart colored with predefined colors in Maple: " }}{SECT 1 {PARA 4 "" 
0 "" {TEXT -1 38 "Create a vector of  predefined colors:" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 230 "col:=[\naquamarine,black,blue,navy
,coral,cyan,brown,gold,green,gray,\ngrey,khaki,magenta,maroon,orange,p
ink,plum,red,sienna,tan,\nturquoise,violet,wheat,white,yellow\n]:\ntex
t := (x0,y0,a)->textplot([x0,y0,`a`], font=[TIMES,ROMAN,18]):" }}}}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 63 "The colored piechart using piesli
ce from the plottools package:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 233 "with(plottools):\ncolpie:=k-> pieslice([0,0], 1.4,2*k*Pi/25..2*
(k+1)*Pi/25, color=col[k]):\ndisplay(\{seq(colpie(k),k=1..25),\nseq( t
ext(2*cos(2*(k+1/2)*Pi/25),2*sin(2*(k+1/2)*Pi/25), col[k]),k=1..25) \}
, \nscaling=constrained, axes=none);" }}{PARA 7 "" 1 "" {TEXT -1 43 "W
arning, the name arrow has been redefined\n" }}}}{SECT 1 {PARA 4 "" 0 
"" {TEXT -1 41 "The colored piechart using polygons only:" }}{EXCHG 
{PARA 265 "> " 0 "" {MPLTEXT 1 0 277 "r:=1.4:\ndisplay(\n\{ seq( polyg
onplot(\n[ [0,0],[r*cos(2*k*Pi/25),r*sin(2*k*Pi/25)],\n[r*cos(2*(k+1)*
Pi/25),r*sin(2*(k+1)*Pi/25)] ],\ncolor=col[k]), k=1..25),\nseq( text(2
*cos(2*k*Pi/25),2*sin(2*k*Pi/25), col[k]),k=1..25) \},\naxes=none, sca
ling=constrained,\ntitle=`Colored Piechart`);" }}}}}{SECT 1 {PARA 3 "
" 0 "" {TEXT -1 66 "The next graphics is an illustration for the Lunes
 of Hyppocrates." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "hyp1 := \+
plot([cos(t),sin(t),t=0..Pi], \nthickness=3, color=red):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "hyp2 := plot([cos(t),sin(t),t=Pi..2
*Pi], \nthickness=3, color=orange):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 89 "hyp3 := plot([sqrt(2)*cos(t), sqrt(2)*sin(t)-1, t=Pi/
4..3*Pi/4],\nthickness=3, color=red):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 131 "hyp4 := polygonplot(\n[ [-1,0],[1,0],[0,-1],[-1,0] ]
,\nthickness=3, color=COLOR(RGB, 0.1960, 0.6000, 0.8000),\nstyle=line,
 axes=none):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "hyp5 := plo
t([sqrt(2)*cos(t), sqrt(2)*sin(t)-1, t=Pi/4..3*Pi/4],\nthickness=3, co
lor=red):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "hyp5 := polyg
onplot(\n[ [-1,0],[0,1],[1,0],[0,1],[-1,0] ],\nthickness=3, color=pink
, axes=none, style=line):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
200 "hyp6:=textplot([0,0.69,`A`],color=red):\nhyp7:=textplot([0,-0.44,
`A`],color=COLOR(RGB, 0.1960, 0.6000, 0.8000)):\nhyp8 := textplot(\{ [
-0.5926,0.6038,`B`], [0.5926,0.6038,`B`],\n[-0.0048,0.1825,`2B`] \} ):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 129 "display(\{hyp1,hyp2,hy
p3,hyp4,hyp6,hyp7\},\nfont=[TIMES,ROMAN,24], scaling=constrained, axes
=none,\ntitle=`The Lune of Hyppocrates`);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 130 "display(\{hyp1,hyp2,hyp3,hyp4,hyp5,hyp8\},\nfont=[
TIMES,ROMAN,24], scaling=constrained, axes=none,\ntitle=`The Lunes of \+
Hyppocrates`);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 229 "Colored disk
. The plottools package contains a routine to generate colored disks. \+
\nThe calling sequence is: disk([x,y], r, ...) with parameters:\n   [x
,y] - center of the disk\n   r     - radius of the disk (optional, def
ault is 1)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 193 "with(plottool
s):\ndisplay(\{ seq(\ndisk([cos(2*k*Pi/25),sin(2*k*Pi/25)],0.1, \ncolo
r= COLOR(RGB,evalf(cos(k/20)),evalf(sin(k/20)),evalf(sin(k/20)) ) ), \+
\nk=1..25) \},\naxes=none, scaling=constrained);" }}}}{SECT 1 {PARA 3 
"" 0 "" {TEXT -1 16 "Colored vectors:" }}{SECT 1 {PARA 4 "" 0 "" 
{TEXT -1 53 "First we write a macro for vectors using polygonplot:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 410 "colvec := (a,b,r,theta,c1,c
2,c3)->display(\{ \npolygonplot( \n[[a, b],[a+0.95*r*cos(theta),b+0.95
*r*sin(theta)]],\nstyle=line, thickness=3),\npolygonplot(\n[[a+r*cos(t
heta),b+r*sin(theta)], \n [a+r*cos(theta)-0.15*r*cos(theta-Pi/12),\n  \+
b+r*sin(theta)-0.15*r*sin(theta-Pi/12)],\n [a+r*cos(theta)-0.15*r*cos(
theta+Pi/12),\n  b+r*sin(theta)-0.15*r*sin(theta+Pi/12)] ]) \n\},\nsca
ling=constrained, color=COLOR(RGB,c1,c2,c3) ):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 48 "vec := (a,b,r,theta)->colvec(a,b,r,theta,1,1,1
):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "colvec0 := (r,theta,c
1,c2,c3)->colvec(0,0,r,theta,c1,c2,c3):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 36 "vec0 := (r,theta)->vec(0,0,r,theta):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "vec1 := display( [seq(colvec0(sqrt(
3),Pi/6+2*Pi*k/6,1,0,1), k=0..5)] ):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 60 "vec2 := display( [seq(colvec0(1,2*Pi*k/6,0,1,1), k=0.
.6)] ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "display(\{vec1,
vec2\},\nscaling=constrained, axes=none,\ntitlefont=[HELVETICA,BOLD,24
], title=`Vector Figure of G2`);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 
-1 374 "The plottools package  also contains a routine for vectors; th
e calling sequence is\narrow(base, dir, wb, wh, hh)\n with parameters \+
\n   base - base of the arrow, a 2D  point\n   dir  - direction vector
, a 2D point   \n   wb   - width of the body of the arrow\n   wh   - w
idth of the head of the arrow\n   hh   - height of the head of the arr
ow as a ratio of the length of the body" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 314 "with(plottools):\nnewvec1 := display( [seq(\narrow([
0,0],[sqrt(3)*cos(Pi/6+2*Pi*k/6),sqrt(3)*sin(Pi/6+2*Pi*k/6)],.01,.1,.1
5,\ncolor=magenta\n), k=0..5)] ):\nnewvec2 := display( [seq(\narrow([0
,0],[cos(2*Pi*k/6),sin(2*Pi*k/6)],.01,.1,.2,\ncolor=cyan\n), k=0..5)] \+
):\ndisplay(\{newvec1,newvec2\},axes=none,scaling=constrained);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{PARA 3 "" 0 "" {TEXT 
-1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 0 "" }}}{MARK "10 0 0" 83 }
{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }