{VERSION 5 0 "HP RISC UNIX" "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 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 2 0 0 0 0 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 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 261 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 263 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 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 256 "" 0 "" {TEXT -1 47 "Weitere Beispiele zur dr eidimensionalen Graphik" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 38 "restart: with(plots): with(plottools):" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 42 "a) Eine ansteigende logarithmische Spir ale" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "spacecurve([log(t)*cos(t), \+ log(t)*sin(t), t/(20*Pi)], t=1..20*Pi, color=coral, thickness=5, numpo ints=200);" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 12 "(Die Option " } {TEXT 256 14 "numpoints=200 " }{TEXT -1 213 "sorgt daf\374r, da\337 di e Spirale nicht zu eckig aussieht.)\n\nb) Eine um einen Zylinder (um d ie z-Achse) gewickelte Spirale, der besseren Sichtbarkeit wegen mit le icht gr\366\337erem Radius gezeichnet als der Zylinder selbst:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 153 "display([cylinder([0,0,0], \+ 3, 10, color=cyan),\nspacecurve([3.1*cos(t), 3.1*sin(t), (10/(20*Pi))* t], t=0..20*Pi, color=red, thickness=5, numpoints=200)]);" }}}{EXCHG {PARA 259 "" 0 "" {TEXT -1 27 "c) Dasselbe mit einem Kegel" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 190 "display([cone([ 0,0,0], 3, 10, color=cyan),\nspacecurve([3.1*t/(20*Pi)*cos(t), 3*t/(20 *Pi)*sin(t), (10/(20*Pi))*t], t=0..20*Pi, color=red, thickness=5, nump oints=200, orientation=[45, 100])]);" }}}{EXCHG {PARA 260 "" 0 "" {TEXT -1 84 "d) Ein Torus rotiert um eine auf der x-Achse liegende sol ide Achse:\nDa das Kommando " }{TEXT 257 9 "cylinder " }{TEXT -1 63 "e inen Zylinder um die z-Achse zeichnet, mu\337 dieser zun\344chst um " }{XPPEDIT 18 0 "Pi/2;" "6#*&%#PiG\"\"\"\"\"#!\"\"" }{TEXT -1 31 " um d ie y-Achse rotiert werden." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "T := torus([0,0,0], 1, 5, color=magenta):\nZ := rotate(cylinder([ 0,0,-8], 0.5, 16, color=khaki),\n Pi/2, [[0,0,0],[0,1,0]]):" }}} {EXCHG {PARA 263 "" 0 "" {TEXT -1 78 "Vorsicht! Das folgende Kommando \+ kann je nach Rechner mehrere Minuten brauchen!" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "display([seq(display([Z, ro tate(T, Pi/30*n, [[1,0,0], [0,0,0]])]), n=0..30)], insequence=true, sc aling=constrained); " }}}{EXCHG {PARA 261 "" 0 "" {TEXT -1 89 "e) Ein \+ dreidimensionales Gitter, das den Einheitsw\374rfel in 1000 kleine W \374rfel unterteilt:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 275 "spacecurve (\{\nseq(seq([[i/10, j/10, 0], [i/10, j/10, 1]], i=0..10), j=0..10),\n seq(seq([[i/10, 0, j/10], [i/10, 1, j/10]], i=0..10), j=0..10),\nseq(s eq([[0, i/10, j/10], [1, i/10, j/10]], i=0..10), j=0..10)\},\ncolor=bl ue, thickness=1, scaling=constrained, orientation=[-16, 64]);" }}} {EXCHG {PARA 262 "" 0 "" {TEXT -1 67 "Eine Raumkurve kann also auch ei nfach eine Menge von Strecken sein." }{MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 38 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }