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{SECT 0 {PARA 11 "" 1 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 9 
"Math 4530" }}{PARA 257 "" 0 "" {TEXT -1 25 "Playing with plane curves
" }}{PARA 258 "" 0 "" {TEXT -1 17 "Friday Januray 26" }}{PARA 0 "" 0 "
" {TEXT -1 94 "We use the formulas from #9 on page 24 to plot planar c
urves with prescribed planar curvature:" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots):" }
}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been \+
redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "theta:=t->in
t(k(r),r=0..t)+phi;\n   #the integral version of k=\n   #d/ds of theta
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&thetaGR6#%\"tG6\"6$%)operatorG%
&arrowGF(,&-%$intG6$-%\"kG6#%\"rG/F3;\"\"!9$\"\"\"%$phiGF8F(F(F(" }}}
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{MPLTEXT 1 0 99 "F:=s->int(cos(theta(t)),t=0..s)+a;\nG:=s->int(sin(the
ta(t)),t=0..s)+b;\n   #here alpha(s)=[F(s),G(s)]" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"FGR6#%\"sG6\"6$%)operatorG%&arrowGF(,&-%$intG6$-%$c
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" {XPPMATH 20 "6#>%\"GGR6#%\"sG6\"6$%)operatorG%&arrowGF(,&-%$intG6$-%
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "a:=0;b:=0;\n  #start at origin\nphi
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aG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"\"!" }}{PARA 11 "" 
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{MPLTEXT 1 0 33 "k:=r->2;\n   #constant curvature 2" }}{PARA 11 "" 1 "
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" {MPLTEXT 1 0 77 "plot([F(s),G(s),s=0..3*Pi/2],color=black);\n  #shou
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