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234 1 {CSTYLE "" -1 -1 "Time s" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 6 6 2 0 2 0 2 2 -1 1 } {PSTYLE "" -1 235 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 6 6 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 236 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 4 4 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 237 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 4 4 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 238 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 4 4 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 239 1 {CSTYLE "" -1 -1 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 4 4 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 240 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 6 6 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 241 1 {CSTYLE "" -1 -1 "T imes" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 6 6 2 0 2 0 2 2 -1 1 } {PSTYLE "" -1 242 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 6 6 2 0 2 0 2 2 -1 1 }} {SECT 0 {PARA 216 "" 0 "" {TEXT 210 58 "MAPLE WORKSHEET #1: 2d Polygo nplots and Graphic Primitives" }}{SECT 1 {PARA 217 "" 0 "" {TEXT 210 23 "Load the plots package:" }{TEXT 210 0 "" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "with(plots):" }}}}{SECT 1 {PARA 218 "" 0 "" {TEXT 210 50 "Define the vertices of a regular n-sided polygon:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "ngon:=(a,b,r,n)-> \n" }{MPLTEXT 1 0 6 "[seq(\n" }{MPLTEXT 1 0 49 "[a+r*cos(2*Pi*k/n),b+r*sin(2*Pi*k/n)], k = 0..n-1\n" }{MPLTEXT 1 0 3 ") \n" }{MPLTEXT 1 0 2 "]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "ngon0:=n->ngon(0,0,1,n):" }}}{PARA 0 "" 0 "" {TEXT 210 14 "Four octagons:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "polygonplot(\{\n" }{MPLTEXT 1 0 58 "ngon(1,0,1,8),ngo n(0,1,1,8),ngon(-1,0,1,8),ngon(0,-1,1,8)\n" }{MPLTEXT 1 0 14 "\},style =line,\n" }{MPLTEXT 1 0 31 "scaling=constrained,axes=none);" }}}} {SECT 1 {PARA 219 "" 0 "" {TEXT 210 46 "Plot a pentagon with various o ptions/settings:" }}{SECT 1 {PARA 220 "" 0 "" {TEXT 210 39 "Plot the p entagon with various options:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "polygonplot(ngon0(5),\n" }{MPLTEXT 1 0 44 "axes=none, color=cyan , scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " polygonplot(ngon0(5),\n" }{MPLTEXT 1 0 44 "axes=none, color=cyan, scal ing=constrained,\n" }{MPLTEXT 1 0 49 "titlefont=[HELVETICA,BOLD,24], t itle=`Pentagon`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "pent : = polygonplot(ngon0(5),\n" }{MPLTEXT 1 0 44 "axes=none, color=cyan, sc aling=constrained,\n" }{MPLTEXT 1 0 50 "titlefont=[HELVETICA,BOLD,24], title=`Pentagon`):\n" }{MPLTEXT 1 0 14 "display(pent);" }}}}{SECT 1 {PARA 221 "" 0 "" {TEXT 210 9 "Add text:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "tex := textplot([0,0,`Inside a Pentagon`],\n" } {MPLTEXT 1 0 47 "font=[TIMES,ROMAN,38], color=COLOR(RGB,1,1,0)):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "display(\{pent,tex\});" }}}} {SECT 1 {PARA 222 "" 0 "" {TEXT 210 13 "Add boundary:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "wirepent := polygonplot(ngon0(5),\n" } {MPLTEXT 1 0 44 "axes=none, color=red, scaling=constrained, \n" } {MPLTEXT 1 0 39 "style=line, thickness=5, linestyle=2):\n" }{MPLTEXT 1 0 18 "display(wirepent);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "display(\{ pent, wirepent, tex\});" }}}}}{SECT 1 {PARA 223 "" 0 "" {TEXT 210 57 "Create a figure for the proof of the Pythagorean Theore m:" }}{SECT 1 {PARA 224 "" 0 "" {TEXT 210 26 "First create the polygon s:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "pyt1 := polygonplot(\n " }{MPLTEXT 1 0 45 "[ [0,0],[1,2],[3,3],[3,0],[1,0],[1,3],[0,3],\n" } {MPLTEXT 1 0 45 "[0,2],[3,2],[3,3],[1,3],[1,0],[0,0],[0,2] ],\n" } {MPLTEXT 1 0 47 "style=line, thickness=3, color=red, axes=none):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "pyt2 := polygonplot(\n" } {MPLTEXT 1 0 65 "[ [4,0],[7,0],[7,3],[4,3],[4,0],[5,0],[7,1],[6,3],[4, 2],[5,0] ],\n" }{MPLTEXT 1 0 47 "style=line, thickness=3, color=red, a xes=none):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "pyt3 := polyg onplot(\n" }{MPLTEXT 1 0 35 "[ [1,0],[3,0],[3,2],[1,2],[1,0] ],\n" } {MPLTEXT 1 0 29 "color=aquamarine, axes=none):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "pyt4 := polygonplot(\n" }{MPLTEXT 1 0 35 "[ [0, 2],[1,2],[1,3],[0,3],[0,2] ],\n" }{MPLTEXT 1 0 29 "color=aquamarine, a xes=none):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "pyt5 := polyg onplot(\n" }{MPLTEXT 1 0 36 "[ [5,0],[7,1],[6,3],[4,2],[5,0] ], \n" } {MPLTEXT 1 0 29 "color=aquamarine, axes=none):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "pyt6 := textplot(\n" }{MPLTEXT 1 0 62 "\{[0.5,- 0.15,`a`],[4.5,-0.15,`a`],[2,-0.15,`b`],[6,-0.15,`b`],\n" }{MPLTEXT 1 0 34 "[0.53,0.79,`c`],[4.47,0.73,`c`]\},\n" }{MPLTEXT 1 0 24 "font=[CO URIER,BOLD,18]):" }}}}{SECT 1 {PARA 225 "" 0 "" {TEXT 210 33 "Then di splay all these together:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "display(\{pyt1,pyt2,pyt3,pyt4,pyt5,pyt6\},\n" }{MPLTEXT 1 0 22 "scali ng=constrained, \n" }{MPLTEXT 1 0 32 "titlefont=[HELVETICA,BOLD,24], \+ \n" }{MPLTEXT 1 0 42 "title=`Proof of the Pythagorean Theorem`);" }}}} }{SECT 1 {PARA 226 "" 0 "" {TEXT 210 44 "A figure for determining the \+ golden section:" }}{SECT 1 {PARA 227 "" 0 "" {TEXT 210 29 "The vertice s 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 228 "" 0 "" {TEXT 210 69 "The line segments P(1)P(3) and P(2)P(4) intersect on the y-axi s at Q:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "slope:=(P(1)[2]-P (3)[2])/(P(1)[1]-P(3)[1]):\n" }{MPLTEXT 1 0 29 "Q:=[0,P(1)[2]-slope*P( 1)[1]]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "penta := polygon plot([seq(P(n), n=0..4)],\n" }{MPLTEXT 1 0 24 "color=red, thickness=4) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "r1 := polygonplot([[P( 1),Q],[P(4),Q]],\n" }{MPLTEXT 1 0 24 "color=red, thickness=4):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "r2 := polygonplot([P(1),P(4) ],\n" }{MPLTEXT 1 0 25 "color=gold, thickness=4):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 39 "r3 := polygonplot([[P(2),Q],[P(3),Q]],\n" } {MPLTEXT 1 0 25 "color=blue, thickness=4):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 22 "labels := textplot(\{ \n" }{MPLTEXT 1 0 59 "[0.5298 ,0.7311,`1`],[-0.004567,0.3876,`golden section=g`],\n" }{MPLTEXT 1 0 71 "[-0.4439,-0.1386,`1`],[0.3764,-0.5394,`1/g`], [-0.02436,-0.90176,` 1`] \n" }{MPLTEXT 1 0 3 "\},\n" }{MPLTEXT 1 0 23 "font=[TIMES,ROMAN,22 ]):" }}}}{SECT 1 {PARA 229 "" 0 "" {TEXT 210 27 "Display all these tog ether:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "display(\{penta, r 1, r2, r3, labels\},\n" }{MPLTEXT 1 0 44 "style=line, axes=none, scali ng=constrained,\n" }{MPLTEXT 1 0 31 "titlefont=[HELVETICA,BOLD,22]);" }}}}{SECT 1 {PARA 230 "" 0 "" {TEXT 210 26 "Add two similar triangles: " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "r4:=polygonplot([[P(1),Q ,P(4)],[P(2),P(3),Q]],\n" }{MPLTEXT 1 0 24 "style=patch,color=cyan):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "display(\{penta, r1, r2, \+ r3, r4, labels\},\n" }{MPLTEXT 1 0 44 "style=line, axes=none, scaling= constrained,\n" }{MPLTEXT 1 0 47 "titlefont=[HELVETICA,BOLD,24],title= `1+1/g=g`);" }}}}}{SECT 1 {PARA 231 "" 0 "" {TEXT 210 53 "Plot the 96- sided regular polygon with symmetry axes:" }}{SECT 1 {PARA 232 "" 0 "" {TEXT 210 19 "First the polygon: " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "polygonplot(ngon0(96),\n" }{MPLTEXT 1 0 43 "axes=none , color=red, scaling=constrained,\n" }{MPLTEXT 1 0 66 "titlefont=[HELV ETICA,BOLD,24],title=`A 96-sided regular polygon`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot([cos(u), sin(u), u=0..2*Pi],\n" } {MPLTEXT 1 0 50 "numpoints=250, thickness=2, scaling=constrained, \n" }{MPLTEXT 1 0 29 "color=blue, tickmarks=[0,0]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "display(\n" }{MPLTEXT 1 0 38 "\{ polygonplot(ng on0(96), color=red), \n" }{MPLTEXT 1 0 77 "plot([cos(u), sin(u), u=0.. 2*Pi], color=blue, numpoints=500, thickness=2) \},\n" }{MPLTEXT 1 0 52 "view=[0.7039..0.7124,0.7034..0.7109], thickness=2, \n" }{MPLTEXT 1 0 33 "axes=none, scaling=constrained );" }}}}{SECT 1 {PARA 233 "" 0 "" {TEXT 210 14 "Then the axes:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "symmax := (k,l)->polygonplot([ \n" }{MPLTEXT 1 0 40 "[1.2*cos( 2*k*Pi/l),1.2*sin(2*k*Pi/l)], \n" }{MPLTEXT 1 0 41 "[-1.2*cos(2*k*Pi/l ),-1.2*sin(2*k*Pi/l)] \n" }{MPLTEXT 1 0 3 "],\n" }{MPLTEXT 1 0 37 "thi ckness=2, style=line, color=blue):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "display(\{ \n" }{MPLTEXT 1 0 64 "polygonplot(ngon0(5) , style=patch, color=red, transparency=.5),\n" }{MPLTEXT 1 0 26 "seq(s ymmax(k,5), k=0..4) \n" }{MPLTEXT 1 0 3 "\},\n" }{MPLTEXT 1 0 32 "axes =none, scaling=constrained,\n" }{MPLTEXT 1 0 67 "titlefont=[HELVETICA, BOLD,24], title=`Symmety axes of a pentagon`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "display(\{ \n" }{MPLTEXT 1 0 48 "polygonplot(ng on0(96), style=patch, color=red),\n" }{MPLTEXT 1 0 28 "seq(symmax(k,96 ), k=0..95) \n" }{MPLTEXT 1 0 3 "\},\n" }{MPLTEXT 1 0 48 "axes=none, s caling=constrained,transparency=.5,\n" }{MPLTEXT 1 0 66 "titlefont=[HE LVETICA,BOLD,24], title=`Symmetry axes of a 96-gon`);" }}}}}{SECT 1 {PARA 234 "" 0 "" {TEXT 210 17 "Hexagonal tiling:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "hex := (a,b,c1,c2,c3)->polygonplot( \n" } {MPLTEXT 1 0 15 "ngon(a,b,1,6),\n" }{MPLTEXT 1 0 27 "color=COLOR(RGB,c 1,c2,c3)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "display(\{ \n " }{MPLTEXT 1 0 16 "hex(0,0,1,0,0),\n" }{MPLTEXT 1 0 6 "seq( \n" } {MPLTEXT 1 0 61 "hex(sqrt(3)*cos(Pi/6+2*k*Pi/6), sqrt(3)*sin(Pi/6+2*k* Pi/6), \n" }{MPLTEXT 1 0 51 "evalf(sin(k/4)),evalf(cos(k/4)),evalf(sin (k/4))), \n" }{MPLTEXT 1 0 9 "k=1..6) \n" }{MPLTEXT 1 0 3 "\},\n" } {MPLTEXT 1 0 31 "axes=none,scaling=constrained);" }}}}{SECT 1 {PARA 235 "" 0 "" {TEXT 210 51 " Piechart colored with predefined colors in \+ Maple: " }}{SECT 1 {PARA 236 "" 0 "" {TEXT 210 38 "Create a vector of \+ predefined colors:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "col:=[ \n" }{MPLTEXT 1 0 61 "aquamarine,black,blue,navy,coral,cyan,brown,gold ,green,gray,\n" }{MPLTEXT 1 0 59 "grey,khaki,magenta,maroon,orange,pin k,plum,red,sienna,tan,\n" }{MPLTEXT 1 0 36 "turquoise,violet,wheat,whi te,yellow\n" }{MPLTEXT 1 0 3 "]:\n" }{MPLTEXT 1 0 64 "text := (x0,y0,a )->textplot([x0,y0,`a`], font=[TIMES,ROMAN,18]):" }}}}{SECT 1 {PARA 237 "" 0 "" {TEXT 210 63 "The colored piechart using pieslice from the plottools package:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "with( plottools):\n" }{MPLTEXT 1 0 73 "colpie:=k-> pieslice([0,0], 1.4,2*k*P i/25..2*(k+1)*Pi/25, color=col[k]):\n" }{MPLTEXT 1 0 33 "display(\{seq (colpie(k),k=1..25),\n" }{MPLTEXT 1 0 78 "seq( text(2*cos(2*(k+1/2)*Pi /25),2*sin(2*(k+1/2)*Pi/25), col[k]),k=1..25) \}, \n" }{MPLTEXT 1 0 32 "scaling=constrained, axes=none);" }}}}{SECT 1 {PARA 238 "" 0 "" {TEXT 210 41 "The colored piechart using polygons only:" }}{EXCHG {PARA 239 "> " 0 "" {MPLTEXT 1 0 8 "r:=1.4:\n" }{MPLTEXT 1 0 9 "displa y(\n" }{MPLTEXT 1 0 20 "\{ seq( polygonplot(\n" }{MPLTEXT 1 0 45 "[ [0 ,0],[r*cos(2*k*Pi/25),r*sin(2*k*Pi/25)],\n" }{MPLTEXT 1 0 47 "[r*cos(2 *(k+1)*Pi/25),r*sin(2*(k+1)*Pi/25)] ],\n" }{MPLTEXT 1 0 25 "color=col[ k]), k=1..25),\n" }{MPLTEXT 1 0 65 "seq( text(2*cos(2*k*Pi/25),2*sin(2 *k*Pi/25), col[k]),k=1..25) \},\n" }{MPLTEXT 1 0 32 "axes=none, scalin g=constrained,\n" }{MPLTEXT 1 0 26 "title=`Colored Piechart`);" }}}}} {SECT 1 {PARA 240 "" 0 "" {TEXT 210 66 "The next graphics is an illust ration for the Lunes of Hyppocrates." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "hyp1 := plot([cos(t),sin(t),t=0..Pi], \n" }{MPLTEXT 1 0 24 "thickness=3, color=red):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "hyp2 := plot([cos(t),sin(t),t=Pi..2*Pi], \n" }{MPLTEXT 1 0 27 "thickness=3, color=orange):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "hyp3 := plot([sqrt(2)*cos(t), sqrt(2)*sin(t)-1, t=Pi/4..3*Pi/4 ],\n" }{MPLTEXT 1 0 24 "thickness=3, color=red):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "hyp4 := polygonplot(\n" }{MPLTEXT 1 0 32 "[ [ -1,0],[1,0],[0,-1],[-1,0] ],\n" }{MPLTEXT 1 0 55 "thickness=3, color=C OLOR(RGB, 0.1960, 0.6000, 0.8000),\n" }{MPLTEXT 1 0 23 "style=line, ax es=none):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "hyp5 := plot([ sqrt(2)*cos(t), sqrt(2)*sin(t)-1, t=Pi/4..3*Pi/4],\n" }{MPLTEXT 1 0 24 "thickness=3, color=red):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "hyp5 := polygonplot(\n" }{MPLTEXT 1 0 37 "[ [-1,0],[0,1],[1,0],[ 0,1],[-1,0] ],\n" }{MPLTEXT 1 0 48 "thickness=3, color=pink, axes=none , style=line):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "hyp6:=tex tplot([0,0.69,`A`],color=red):\n" }{MPLTEXT 1 0 72 "hyp7:=textplot([0, -0.44,`A`],color=COLOR(RGB, 0.1960, 0.6000, 0.8000)):\n" }{MPLTEXT 1 0 62 "hyp8 := textplot(\{ [-0.5926,0.6038,`B`], [0.5926,0.6038,`B`],\n " }{MPLTEXT 1 0 26 "[-0.0048,0.1825,`2B`] \} ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "display(\{hyp1,hyp2,hyp3,hyp4,hyp6,hyp7\},\n" }{MPLTEXT 1 0 55 "font=[TIMES,ROMAN,24], scaling=constrained, axes=non e,\n" }{MPLTEXT 1 0 33 "title=`The Lune of Hyppocrates`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "display(\{hyp1,hyp2,hyp3,hyp4,hyp5, hyp8\},\n" }{MPLTEXT 1 0 55 "font=[TIMES,ROMAN,24], scaling=constraine d, axes=none,\n" }{MPLTEXT 1 0 34 "title=`The Lunes of Hyppocrates`);" }}}}{SECT 1 {PARA 241 "" 0 "" {TEXT 210 83 "Colored disk. The plottoo ls package contains a routine to generate colored disks. \n" }{TEXT 210 62 "The calling sequence is: disk([x,y], r, ...) with parameters: \n" }{TEXT 210 30 " [x,y] - center of the disk\n" }{TEXT 210 54 " \+ r - radius of the disk (optional, default is 1)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "with(plottools):\n" }{MPLTEXT 1 0 15 "displ ay(\{ seq(\n" }{MPLTEXT 1 0 43 "disk([cos(2*k*Pi/25),sin(2*k*Pi/25)],0 .1, \n" }{MPLTEXT 1 0 74 "color= COLOR(RGB,evalf(cos(k/20)),evalf(sin( k/20)),evalf(sin(k/20)) ) ), \n" }{MPLTEXT 1 0 12 "k=1..25) \},\n" } {MPLTEXT 1 0 32 "axes=none, scaling=constrained);" }}}}{SECT 1 {PARA 242 "" 0 "" {TEXT 210 16 "Colored vectors:" }}{SECT 1 {PARA 4 "" 0 "" {TEXT 212 53 "First we write a macro for vectors using polygonplot:" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "colvec := (a,b,r,theta,c1,c 2,c3)->display(\{ \n" }{MPLTEXT 1 0 14 "polygonplot( \n" }{MPLTEXT 1 0 52 "[[a, b],[a+0.95*r*cos(theta),b+0.95*r*sin(theta)]],\n" }{MPLTEXT 1 0 26 "style=line, thickness=3),\n" }{MPLTEXT 1 0 13 "polygonplot(\n " }{MPLTEXT 1 0 35 "[[a+r*cos(theta),b+r*sin(theta)], \n" }{MPLTEXT 1 0 42 " [a+r*cos(theta)-0.15*r*cos(theta-Pi/12),\n" }{MPLTEXT 1 0 43 " \+ b+r*sin(theta)-0.15*r*sin(theta-Pi/12)],\n" }{MPLTEXT 1 0 42 " [a+r*c os(theta)-0.15*r*cos(theta+Pi/12),\n" }{MPLTEXT 1 0 46 " b+r*sin(thet a)-0.15*r*sin(theta+Pi/12)] ]) \n" }{MPLTEXT 1 0 3 "\},\n" }{MPLTEXT 1 0 49 "scaling=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,c1,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(colvec 0(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 21 "display(\{vec 1,vec2\},\n" }{MPLTEXT 1 0 32 "scaling=constrained, axes=none,\n" } {MPLTEXT 1 0 60 "titlefont=[HELVETICA,BOLD,24], title=`Vector Figure o f G2`);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 212 84 "The plottools packa ge also contains a routine for vectors; the calling sequence is\n" } {TEXT 212 29 "arrow(base, dir, wb, wh, hh)\n" }{TEXT 212 18 " with par ameters \n" }{TEXT 212 41 " base - base of the arrow, a 2D point\n" }{TEXT 212 42 " dir - direction vector, a 2D point \n" }{TEXT 212 41 " wb - width of the body of the arrow\n" }{TEXT 212 41 " \+ wh - width of the head of the arrow\n" }{TEXT 212 78 " hh - heig ht of the head of the arrow as a ratio of the length of the body" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "with(plottools):\n" } {MPLTEXT 1 0 26 "newvec1 := display( [seq(\n" }{MPLTEXT 1 0 80 "arrow( [0,0],[sqrt(3)*cos(Pi/6+2*Pi*k/6),sqrt(3)*sin(Pi/6+2*Pi*k/6)],.01,.1,. 15,\n" }{MPLTEXT 1 0 14 "color=magenta\n" }{MPLTEXT 1 0 15 "), k=0..5) ] ):\n" }{MPLTEXT 1 0 26 "newvec2 := display( [seq(\n" }{MPLTEXT 1 0 53 "arrow([0,0],[cos(2*Pi*k/6),sin(2*Pi*k/6)],.01,.1,.2,\n" }{MPLTEXT 1 0 11 "color=cyan\n" }{MPLTEXT 1 0 15 "), k=0..5)] ):\n" }{MPLTEXT 1 0 57 "display(\{newvec1,newvec2\},axes=none,scaling=constrained);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{PARA 3 "" 0 "" {TEXT 213 0 "" }}{PARA 3 "" 0 "" {TEXT 213 0 "" }}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 15 10 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }