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"Courier" 1 16 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 296 1 {CSTYLE "" -1 -1 "Courier" 1 16 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 297 1 {CSTYLE "" -1 -1 "Courier" 1 16 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 298 1 {CSTYLE "" -1 -1 "Cou rier" 1 16 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 299 1 {CSTYLE "" -1 -1 "Courier" 1 16 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 300 1 {CSTYLE "" -1 -1 "Times" 1 16 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 4 4 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 301 1 {CSTYLE "" -1 -1 "Courier" 1 16 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 302 1 {CSTYLE "" -1 -1 "Courier" 1 16 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }} {SECT 0 {PARA 215 "" 0 "" {TEXT 210 34 "MAPLE WORKSHEET #3: 2d Animat ions." }}{SECT 1 {PARA 216 "" 0 "" {TEXT 213 22 "Load the plots packag e" }}{EXCHG {PARA 217 "> " 0 "" {MPLTEXT 1 0 13 "with(plots):\n" } {MPLTEXT 1 0 42 "setoptions(scaling=constrained,axes=none):" }}}} {SECT 1 {PARA 218 "" 0 "" {TEXT 213 30 "Animate a simple function plot " }}{EXCHG {PARA 219 "> " 0 "" {MPLTEXT 1 0 36 "animate(sin(x*t), x=-1 0..10,t=1..2,\n" }{MPLTEXT 1 0 50 "thickness=3, color=red, numpoints=2 00, frames=20);" }}}}{SECT 1 {PARA 220 "" 0 "" {TEXT 213 24 "Animate p arametric plots" }}{SECT 1 {PARA 221 "" 0 "" {TEXT 214 46 "Animate a r olling circle as a parametric plot:" }}{EXCHG {PARA 222 "> " 0 "" {MPLTEXT 1 0 48 "animate([t+cos(u),sin(u),u=0..2*Pi], t=0..2*Pi,\n" } {MPLTEXT 1 0 35 "color=red, thickness=3, frames=30);" }}}}{SECT 1 {PARA 223 "" 0 "" {TEXT 214 21 "With background plot:" }}{EXCHG {PARA 224 "> " 0 "" {MPLTEXT 1 0 10 "display(\{\n" }{MPLTEXT 1 0 50 "animate ([t+cos(u),1+sin(u),u=0..2*Pi], t=0..2*Pi,\n" }{MPLTEXT 1 0 36 "color= red, thickness=3, frames=20),\n" }{MPLTEXT 1 0 32 "plot(0,x=-1..2*Pi+1 ,color=blue,\n" }{MPLTEXT 1 0 14 "thickness=3) \n" }{MPLTEXT 1 0 3 "\} );" }}}}{SECT 1 {PARA 225 "" 0 "" {TEXT 214 20 "Combined animations:" }}{EXCHG {PARA 226 "> " 0 "" {MPLTEXT 1 0 11 "animate(\{ \n" }{MPLTEXT 1 0 62 "[cos(t)+0.05*cos(u),sin(t)+0.05*sin(u), u=0..2*Pi,color=red], \n" }{MPLTEXT 1 0 42 "[(u-0.05)*cos(t),(u-0.05)*sin(t),u=0..1] \n" } {MPLTEXT 1 0 4 "\}, \n" }{MPLTEXT 1 0 11 "t=0..2*Pi,\n" }{MPLTEXT 1 0 35 "color=red, thickness=3, frames=20);" }}}}{SECT 1 {PARA 227 "" 0 "" {TEXT 214 17 "Rotating segment:" }}{EXCHG {PARA 228 "> " 0 "" {MPLTEXT 1 0 9 "animate(\n" }{MPLTEXT 1 0 30 "[cos(t)*u,sin(t)*u,u=-2. .2], \n" }{MPLTEXT 1 0 11 "t=0..2*Pi,\n" }{MPLTEXT 1 0 42 "color=aquam arine, thickness=3, frames=20);" }}}}}{SECT 1 {PARA 229 "" 0 "" {TEXT 213 27 "Drawing curves by animation" }}{EXCHG {PARA 230 "> " 0 "" {MPLTEXT 1 0 47 "animate([cos(t*u),sin(t*u),u=0..1], t=0..2*Pi,\n" } {MPLTEXT 1 0 35 "color=red, thickness=3, frames=20);" }}}{SECT 1 {PARA 231 "" 0 "" {TEXT 214 32 "Animation with multiple display:" }} {EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 10 "display(\{\n" }{MPLTEXT 1 0 9 "animate(\n" }{MPLTEXT 1 0 29 "[cos(t)*u,sin(t)*u,u=0..1], \n" } {MPLTEXT 1 0 11 "t=0..2*Pi,\n" }{MPLTEXT 1 0 16 "color=magenta),\n" } {MPLTEXT 1 0 9 "animate(\n" }{MPLTEXT 1 0 29 "[cos(t*u),sin(t*u),u=0.. 1], \n" }{MPLTEXT 1 0 11 "t=0..2*Pi,\n" }{MPLTEXT 1 0 12 "color=blue) \n" }{MPLTEXT 1 0 4 "\}, \n" }{MPLTEXT 1 0 13 "thickness=3);" }}}}} {SECT 1 {PARA 233 "" 0 "" {TEXT 213 23 "Animate the the cycloid" }} {EXCHG {PARA 234 "> " 0 "" {MPLTEXT 1 0 19 "circle := animate(\n" } {MPLTEXT 1 0 32 "[t+cos(u),1+sin(u),u=0..2*Pi], \n" }{MPLTEXT 1 0 11 " t=0..3*Pi,\n" }{MPLTEXT 1 0 23 "color=cyan, frames=20):" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 0 31 "base := plot(0, x=-1..3*Pi+1, \n" }{MPLTEXT 1 0 12 "color=blue):" }}}{EXCHG {PARA 236 "> " 0 "" {MPLTEXT 1 0 24 "display(\{circle, base\},\n" }{MPLTEXT 1 0 13 "thickn ess=3);" }}}{EXCHG {PARA 237 "> " 0 "" {MPLTEXT 1 0 34 "P:=(t,l)->[t-l *sin(t),1-l*cos(t)]:" }}}{EXCHG {PARA 238 "> " 0 "" {MPLTEXT 1 0 20 "c yc := l->animate(\{\n" }{MPLTEXT 1 0 31 "[u*P(t,l)[1]+(1-u)*P(t,0)[1], \n" }{MPLTEXT 1 0 38 "u*P(t,l)[2]+(1-u)*P(t,0)[2], u=0..1],\n" } {MPLTEXT 1 0 36 "[P(t*u,l)[1], P(t*u,l)[2], u=0..1] \n" }{MPLTEXT 1 0 13 "\},t=0..3*Pi,\n" }{MPLTEXT 1 0 22 "color=red, frames=20):" }}} {EXCHG {PARA 239 "> " 0 "" {MPLTEXT 1 0 32 "display(\{circle, base, cy c(1)\},\n" }{MPLTEXT 1 0 13 "thickness=3);" }}}{EXCHG {PARA 240 "> " 0 "" {MPLTEXT 1 0 33 "display(\{circle, base, cyc(.5)\},\n" }{MPLTEXT 1 0 13 "thickness=3);" }}}{EXCHG {PARA 241 "> " 0 "" {MPLTEXT 1 0 34 " display(\{circle, base, cyc(1.5)\},\n" }{MPLTEXT 1 0 13 "thickness=3); " }}}}{SECT 1 {PARA 242 "" 0 "" {TEXT 213 26 "Animate the the epicyclo id" }}{EXCHG {PARA 243 "> " 0 "" {MPLTEXT 1 0 29 "rolloncircle := r->a nimate( \n" }{MPLTEXT 1 0 24 "[(1+r)*cos(t)+r*cos(u),\n" }{MPLTEXT 1 0 23 "(1+r)*sin(t)+r*sin(u),\n" }{MPLTEXT 1 0 13 "u=0..2*Pi], \n" } {MPLTEXT 1 0 11 "t=0..2*Pi,\n" }{MPLTEXT 1 0 23 "color=cyan, frames=20 ):" }}}{EXCHG {PARA 244 "> " 0 "" {MPLTEXT 1 0 19 "basecircle:= plot( \n" }{MPLTEXT 1 0 28 "[cos(u),sin(u),u=0..2*Pi], \n" }{MPLTEXT 1 0 12 "color=blue):" }}}{EXCHG {PARA 245 "> " 0 "" {MPLTEXT 1 0 11 "display( \{ \n" }{MPLTEXT 1 0 30 "basecircle, rolloncircle(1/2)\n" }{MPLTEXT 1 0 3 "\},\n" }{MPLTEXT 1 0 13 "thickness=3);" }}}{EXCHG {PARA 246 "> " 0 "" {MPLTEXT 1 0 13 "Q:=(t,r,l)->\n" }{MPLTEXT 1 0 32 "[(1+r)*cos(t)- l*cos((1+1/r)*t),\n" }{MPLTEXT 1 0 31 "(1+r)*sin(t)-l*sin((1+1/r)*t)]: " }}}{EXCHG {PARA 247 "> " 0 "" {MPLTEXT 1 0 20 "epicycle := (r,l)->\n " }{MPLTEXT 1 0 11 "animate(\{ \n" }{MPLTEXT 1 0 34 "[u*Q(t,r,l)[1]+(1 -u)*Q(t,r,0)[1],\n" }{MPLTEXT 1 0 41 "u*Q(t,r,l)[2]+(1-u)*Q(t,r,0)[2], u=0..1],\n" }{MPLTEXT 1 0 38 "[Q(t*u,r,l)[1],Q(t*u,r,l)[2],u=0..1] \n" }{MPLTEXT 1 0 13 "\},t=0..2*Pi,\n" }{MPLTEXT 1 0 37 "numpoints=200, c olor=red, frames=20):" }}}{EXCHG {PARA 248 "> " 0 "" {MPLTEXT 1 0 59 " display(\{basecircle, rolloncircle(1/2),epicycle(1/2,3/2)\},\n" } {MPLTEXT 1 0 13 "thickness=3);" }}}{EXCHG {PARA 249 "> " 0 "" {MPLTEXT 1 0 21 "display(\{basecircle,\n" }{MPLTEXT 1 0 36 "rolloncircle(1/4), epicycle(1/4,2)\},\n" }{MPLTEXT 1 0 13 "thickness=3);" }}}}{SECT 1 {PARA 250 "" 0 "" {TEXT 213 27 "Animate the the hypocycloid" }}{EXCHG {PARA 251 "> " 0 "" {MPLTEXT 1 0 28 "rollincircle := r->animate(\n" } {MPLTEXT 1 0 46 "[(1-r)*cos(t)+r*cos(u),(1-r)*sin(t)+r*sin(u),\n" } {MPLTEXT 1 0 12 "u=0..3*Pi],\n" }{MPLTEXT 1 0 11 "t=0..2*Pi,\n" } {MPLTEXT 1 0 23 "color=cyan, frames=20):" }}}{EXCHG {PARA 252 "> " 0 " " {MPLTEXT 1 0 21 "display(basecircle, \n" }{MPLTEXT 1 0 19 "rollincir cle(1/2),\n" }{MPLTEXT 1 0 13 "thickness=3);" }}}{EXCHG {PARA 253 "> " 0 "" {MPLTEXT 1 0 14 "R:=(t,r,l)->[\n" }{MPLTEXT 1 0 31 "(1-r)*cos(t) +l*cos((1-1/r)*t),\n" }{MPLTEXT 1 0 30 "(1-r)*sin(t)+l*sin((1-1/r)*t) \n" }{MPLTEXT 1 0 2 "]:" }}}{EXCHG {PARA 254 "> " 0 "" {MPLTEXT 1 0 29 "hypocycle := (r,l)->animate(\n" }{MPLTEXT 1 0 36 "\{ [u*R(t,r,l)[1 ]+(1-u)*R(t,r,0)[1],\n" }{MPLTEXT 1 0 41 "u*R(t,r,l)[2]+(1-u)*R(t,r,0) [2],u=0..1],\n" }{MPLTEXT 1 0 41 "[R(t*u,r,l)[1],R(t*u,r,l)[2],u=0..1] \}, \n" }{MPLTEXT 1 0 11 "t=0..2*Pi,\n" }{MPLTEXT 1 0 37 "numpoints=2 00, color=red, frames=20):" }}}{EXCHG {PARA 255 "> " 0 "" {MPLTEXT 1 0 21 "display(\{basecircle,\n" }{MPLTEXT 1 0 37 "rollincircle(1/4),hyp ocycle(1/4,1/4)\n" }{MPLTEXT 1 0 3 "\},\n" }{MPLTEXT 1 0 31 "insequenc e=false, thickness=3,\n" }{MPLTEXT 1 0 30 "title=`The Astroid Animated `);" }}}{EXCHG {PARA 256 "> " 0 "" {MPLTEXT 1 0 21 "display(\{basecirc le,\n" }{MPLTEXT 1 0 39 "rollincircle(1/3),hypocycle(1/3,2/3)\},\n" } {MPLTEXT 1 0 13 "thickness=3);" }}}}{SECT 1 {PARA 257 "" 0 "" {TEXT 213 18 "Rotate a pentagon" }}{EXCHG {PARA 258 "> " 0 "" {MPLTEXT 1 0 17 "with(plottools):\n" }{MPLTEXT 1 0 17 "rotpentagon:=t->\n" } {MPLTEXT 1 0 8 "rotate(\n" }{MPLTEXT 1 0 14 "polygonplot([\n" } {MPLTEXT 1 0 44 "seq([cos(2*k*Pi/5), sin(2*k*Pi/5)], k=0..4)\n" } {MPLTEXT 1 0 29 "], color=cyan, style=patch),\n" }{MPLTEXT 1 0 4 "t): \n" }{MPLTEXT 1 0 10 "display([\n" }{MPLTEXT 1 0 35 "seq(rotpentagon(t *Pi/20), t=0..40)\n" }{MPLTEXT 1 0 3 "],\n" }{MPLTEXT 1 0 18 "insequen ce=false,\n" }{MPLTEXT 1 0 18 "transparency=0.5);" }}}}{SECT 1 {PARA 259 "" 0 "" {TEXT 213 17 "Rotate a segment " }}{EXCHG {PARA 260 "> " 0 "" {MPLTEXT 1 0 20 "rotseg:=t->display(\{" }{MPLTEXT 1 0 1 "\n" } {MPLTEXT 1 0 8 "rotate(\n" }{MPLTEXT 1 0 41 "line([0,0],[0,1],color=re d,thickness=3),\n" }{MPLTEXT 1 0 2 "t)" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 3 "\}):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 261 "> " 0 "" {MPLTEXT 1 0 10 "display([\n" }{MPLTEXT 1 0 30 "seq(rotseg(-t*Pi/20),t =0..10)\n" }{MPLTEXT 1 0 3 "],\n" }{MPLTEXT 1 0 17 "insequence=true);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 262 "> " 0 "" {MPLTEXT 1 0 25 "rot segment:=t->display(\{\n" }{MPLTEXT 1 0 11 "translate(\n" }{MPLTEXT 1 0 8 "rotate(\n" }{MPLTEXT 1 0 41 "line([0,0],[0,1],color=red,thickness =3),\n" }{MPLTEXT 1 0 4 "t),\n" }{MPLTEXT 1 0 7 ".5,0),\n" }{MPLTEXT 1 0 5 "line(" }{MPLTEXT 1 0 40 "[-0.5,0],[0.5,0],color=red,thickness=3 )\n" }{MPLTEXT 1 0 2 "\})" }{MPLTEXT 1 0 1 ":" }}}{EXCHG {PARA 263 "> " 0 "" {MPLTEXT 1 0 10 "display([\n" }{MPLTEXT 1 0 24 "seq(rotsegment( -t*Pi/20)" }{MPLTEXT 1 0 10 ",t=0..10)\n" }{MPLTEXT 1 0 3 "],\n" } {MPLTEXT 1 0 15 "insequence=true" }{MPLTEXT 1 0 2 ");" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 264 "> " 0 "" {MPLTEXT 1 0 26 "rotsegments:=t->di splay(\{\n" }{MPLTEXT 1 0 11 "translate(\n" }{MPLTEXT 1 0 8 "rotate(\n " }{MPLTEXT 1 0 41 "line([0,0],[0,1],color=red,thickness=3),\n" } {MPLTEXT 1 0 1 "-" }{MPLTEXT 1 0 4 "t),\n" }{MPLTEXT 1 0 7 ".5,0),\n" }{MPLTEXT 1 0 11 "translate(\n" }{MPLTEXT 1 0 8 "rotate(\n" }{MPLTEXT 1 0 41 "line([0,0],[0,1],color=red,thickness=3),\n" }{MPLTEXT 1 0 4 "t ),\n" }{MPLTEXT 1 0 1 "-" }{MPLTEXT 1 0 6 ".5,0)," }{MPLTEXT 1 0 1 "\n " }{MPLTEXT 1 0 45 "line([-0.5,0],[0.5,0],color=red,thickness=3)\n" } {MPLTEXT 1 0 3 "\}):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 265 "> " 0 "" {MPLTEXT 1 0 10 "display([\n" }{MPLTEXT 1 0 34 "seq(rotsegments(t*Pi/ 20),t=0..10)\n" }{MPLTEXT 1 0 3 "],\n" }{MPLTEXT 1 0 15 "insequence=tr ue" }{MPLTEXT 1 0 2 ");" }{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 266 "" 0 "" {TEXT 213 22 "Examples of animations" }}{SECT 0 {PARA 267 "" 0 "" {TEXT 214 16 "Throwing a ball:" }}{EXCHG {PARA 268 "> " 0 "" {MPLTEXT 1 0 16 "with(plottools):" }}}{EXCHG {PARA 269 "> " 0 "" {MPLTEXT 1 0 9 "display(\n" }{MPLTEXT 1 0 14 "[display(seq(\n" }{MPLTEXT 1 0 31 "di sk([i,100-i^2],3,color=red),\n" }{MPLTEXT 1 0 12 "i=-10..10),\n" } {MPLTEXT 1 0 44 "axes=none,tickmarks=[0,0],insequence=true),\n" } {MPLTEXT 1 0 43 "polygonplot([[7,0],[13,0],[13,-3],[7,-3]],\n" } {MPLTEXT 1 0 14 "color=wheat),\n" }{MPLTEXT 1 0 47 "polygonplot([[-7,0 ],[-13,0],[-13,-3],[-7,-3]],\n" }{MPLTEXT 1 0 16 "color=maroon)]);" }} }}{SECT 0 {PARA 270 "" 0 "" {TEXT 214 10 "Collision:" }}{EXCHG {PARA 271 "> " 0 "" {MPLTEXT 1 0 9 "display(\n" }{MPLTEXT 1 0 14 "[seq(ellip se(\n" }{MPLTEXT 1 0 22 "[0,6-i],1,1),i=1..4),\n" }{MPLTEXT 1 0 13 "se q(ellipse(\n" }{MPLTEXT 1 0 25 "[0,1/i],1,1/i),i=1..10),\n" }{MPLTEXT 1 0 13 "seq(ellipse(\n" }{MPLTEXT 1 0 35 "[0,1/(11-i)],1,1/(11-i)),i=1 ..10),\n" }{MPLTEXT 1 0 13 "seq(ellipse(\n" }{MPLTEXT 1 0 21 "[0,i],1, 1),i=2..5)],\n" }{MPLTEXT 1 0 17 "insequence=true,\n" }{MPLTEXT 1 0 28 "thickness=2, color=magenta);" }}}}{SECT 0 {PARA 272 "" 0 "" {TEXT 214 17 "Lissajous curves:" }}{EXCHG {PARA 273 "> " 0 "" {MPLTEXT 1 0 50 "plot([sin(2*x),sin(3*x),x=0..2*Pi],numpoints=100,\n" }{MPLTEXT 1 0 50 "thickness=2,color=navy,title=`Lissajous curve I`);" }}}{EXCHG {PARA 274 "> " 0 "" {MPLTEXT 1 0 50 "plot([sin(5*x),sin(6*x),x=0..2*Pi ],numpoints=100,\n" }{MPLTEXT 1 0 51 "thickness=2,color=navy,title=`Li ssajous curve II`);" }}}{EXCHG {PARA 275 "> " 0 "" {MPLTEXT 1 0 43 "an imate([sin(2*t*x),sin(3*t*x),t=0..2*Pi],\n" }{MPLTEXT 1 0 32 "x=0..1,n umpoints=100,frames=32,\n" }{MPLTEXT 1 0 61 "thickness=2,color=navy,ti tle=`Lissajous curve animated III`);" }}}{EXCHG {PARA 276 "> " 0 "" {MPLTEXT 1 0 43 "animate([sin(5*t*x),sin(6*t*x),t=0..2*Pi],\n" } {MPLTEXT 1 0 32 "x=0..1,numpoints=200,frames=32,\n" }{MPLTEXT 1 0 60 " thickness=2,color=navy,title=`Lissajous curve animated IV`);" }}}} {SECT 0 {PARA 277 "" 0 "" {TEXT 214 20 "Animation in arrays:" }} {EXCHG {PARA 278 "> " 0 "" {MPLTEXT 1 0 16 "P:=x->display(\{\n" } {MPLTEXT 1 0 81 "polygonplot([[1.1,1.1],[-1.1,1.1],[-1.1,-1.1],[1.1,-1 .1]],color=blue,style=line)," }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 60 "p lot([sin(5*t*x/10),sin(6*t*x/10),t=0..2*Pi],numpoints=100)\n" } {MPLTEXT 1 0 3 "\}):" }}}{EXCHG {PARA 279 "> " 0 "" {MPLTEXT 1 0 22 "A := array(1..2,1..5,\n" }{MPLTEXT 1 0 21 "[[seq(P(n),n=1..5)],\n" } {MPLTEXT 1 0 22 "[seq(P(n),n=6..10)]]):" }}}{EXCHG {PARA 280 "> " 0 "" {MPLTEXT 1 0 11 "display(A,\n" }{MPLTEXT 1 0 13 "thickness=2);" }}} {EXCHG {PARA 281 "> " 0 "" {MPLTEXT 1 0 16 "Q:=x->display(\{\n" } {MPLTEXT 1 0 81 "polygonplot([[1.1,1.1],[-1.1,1.1],[-1.1,-1.1],[1.1,-1 .1]],color=blue,style=line)," }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 46 "p lot([sin(5*t*x/20),sin(6*t*x/20),t=0..2*Pi],\n" }{MPLTEXT 1 0 15 "nump oints=100)\n" }{MPLTEXT 1 0 3 "\}):" }}}{EXCHG {PARA 282 "> " 0 "" {MPLTEXT 1 0 22 "B := array(1..4,1..5,\n" }{MPLTEXT 1 0 21 "[[seq(Q(n) ,n=1..5)],\n" }{MPLTEXT 1 0 21 "[seq(Q(n),n=6..10)],\n" }{MPLTEXT 1 0 22 "[seq(Q(n),n=11..15)],\n" }{MPLTEXT 1 0 21 "[seq(Q(n),n=16..20)]\n" }{MPLTEXT 1 0 3 "]):" }}}{EXCHG {PARA 283 "> " 0 "" {MPLTEXT 1 0 11 " display(B,\n" }{MPLTEXT 1 0 13 "thickness=2);" }}}{EXCHG {PARA 284 "> " 0 "" {MPLTEXT 1 0 22 "B := array(1..4,1..5,\n" }{MPLTEXT 1 0 38 "[se q([seq(Q(n+5*k),n=1..5)],k=0..3)]):" }}}{EXCHG {PARA 285 "> " 0 "" {MPLTEXT 1 0 11 "display(B,\n" }{MPLTEXT 1 0 13 "thickness=2);" }}} {EXCHG {PARA 286 "> " 0 "" {MPLTEXT 1 0 10 "display([\n" }{MPLTEXT 1 0 55 "display(seq(Q(n),n=1..20),insequence=true,thickness=2)\n" } {MPLTEXT 1 0 3 "]);" }}}}}{SECT 1 {PARA 287 "" 0 "" {TEXT 213 32 "Rota te a vector and the pentagon" }}{EXCHG {PARA 288 "> " 0 "" {MPLTEXT 1 0 15 "rotvector:=t->\n" }{MPLTEXT 1 0 61 "display(arrow([0,0], [cos(t) ,sin(t)],.01,.1,.2, color=blue)):" }}}{EXCHG {PARA 289 "> " 0 "" {MPLTEXT 1 0 44 "display([seq(rotvector(t*Pi/10), t=0..20)],\n" } {MPLTEXT 1 0 17 "insequence=true);" }}}{EXCHG {PARA 290 "> " 0 "" {MPLTEXT 1 0 18 "newrotvector:=t->\n" }{MPLTEXT 1 0 8 "rotate(\n" } {MPLTEXT 1 0 52 "display(arrow([0,0], [1,0],.01,.1,.2, color=blue)),\n " }{MPLTEXT 1 0 3 "t):" }}}{EXCHG {PARA 291 "> " 0 "" {MPLTEXT 1 0 47 "display([seq(newrotvector(t*Pi/10), t=0..20)],\n" }{MPLTEXT 1 0 17 "i nsequence=true);" }}}{EXCHG {PARA 292 "> " 0 "" {MPLTEXT 1 0 21 "rotst ructure := t ->\n" }{MPLTEXT 1 0 8 "rotate(\n" }{MPLTEXT 1 0 53 "displ ay(\{arrow([0,0], [.9,0],.01,.1,.2, color=blue),\n" }{MPLTEXT 1 0 14 " polygonplot([\n" }{MPLTEXT 1 0 44 "seq([cos(2*k*Pi/5), sin(2*k*Pi/5)], k=0..4)\n" }{MPLTEXT 1 0 47 "], color=cyan, style=patch,transparency= .5)\}),\n" }{MPLTEXT 1 0 3 "t):" }}}{EXCHG {PARA 293 "> " 0 "" {MPLTEXT 1 0 47 "display([seq(rotstructure(t*Pi/10), t=0..20)],\n" } {MPLTEXT 1 0 17 "insequence=true);" }}}}{SECT 1 {PARA 294 "" 0 "" {TEXT 213 19 "Transforming curves" }}{EXCHG {PARA 295 "> " 0 "" {MPLTEXT 1 0 7 "a:=t->\n" }{MPLTEXT 1 0 38 "plot([[(1-t)*sin(2*x)+t*(3 +sin(5*x)),\n" }{MPLTEXT 1 0 38 " (1-t)*sin(3*x)+t*(3+sin(6*x)), \n" }{MPLTEXT 1 0 12 "x=0..2*Pi],\n" }{MPLTEXT 1 0 31 "[sin(2*x),sin(3 *x),x=0..2*Pi],\n" }{MPLTEXT 1 0 34 "[3+sin(5*x),3+sin(6*x),x=0..2*Pi] \n" }{MPLTEXT 1 0 59 "], color=[red,blue,green],thickness=[3,2,2],nump oints=100):" }}}{EXCHG {PARA 296 "> " 0 "" {MPLTEXT 1 0 48 "display([s eq(a(t/20),t=0..20)],insequence=true);" }}}{EXCHG {PARA 297 "> " 0 "" {MPLTEXT 1 0 10 "display([\n" }{MPLTEXT 1 0 46 "display(seq(a(t/20),t= 1..19),insequence=true)\n" }{MPLTEXT 1 0 3 "]);" }}}{EXCHG {PARA 298 " > " 0 "" {MPLTEXT 1 0 7 "b:=t->\n" }{MPLTEXT 1 0 34 "plot([[(1-t)*sin( 2*x)+t*sin(5*x),\n" }{MPLTEXT 1 0 34 " (1-t)*sin(3*x)+t*sin(6*x) ,\n" }{MPLTEXT 1 0 11 "x=0..2*Pi]\n" }{MPLTEXT 1 0 59 "], color=[red,b lue,green],thickness=[3,2,2],numpoints=100):" }}}{EXCHG {PARA 299 "> " 0 "" {MPLTEXT 1 0 48 "display([seq(b(t/20),t=0..20)],insequence=true) ;" }}}{SECT 1 {PARA 300 "" 0 "" {TEXT 214 11 "Smile-frown" }}{EXCHG {PARA 301 "> " 0 "" {MPLTEXT 1 0 19 "face:=t->display(\{\n" }{MPLTEXT 1 0 57 "plot([.6+.4*cos(u),1.5+.2*sin(u),u=0..2*Pi],color=blue),\n" } {MPLTEXT 1 0 57 "plot([-.6+.4*cos(u),1.5+.2*sin(u),u=0..2*Pi],color=bl ue)," }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 50 "plot([2*cos(u),1+2*sin(u) ,u=0..2*Pi],color=gold),\n" }{MPLTEXT 1 0 6 "plot(\n" }{MPLTEXT 1 0 40 "[cos(u),t*sin(u),u=Pi..2*Pi],color=red)\n" }{MPLTEXT 1 0 3 "\}):" }}}{EXCHG {PARA 302 "> " 0 "" {MPLTEXT 1 0 10 "display([\n" }{MPLTEXT 1 0 42 "seq(face(t/10),t=-5..5)],insequence=true,\n" }{MPLTEXT 1 0 13 "thickness=3);" }}}}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 15 10 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }