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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 259 "" 0 "" {TEXT -1 12 "Pedal Curves" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 223 "Here is an example to show h
ow to use Maple to calculate and draw\nthe pedal curve    ( q1(t), q2(
t) )  associated to a given curve  ( p1(t), p2(t) ).\n\n\nFirst we sup
ply the data for   the   original curve   ( p1(t), p2(t) )\n" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 49 "p1 := cos(t)+1; p2 := sin(t); a := 0; b :
= 2*Pi; " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "\n\nNow we calculate \+
the  velocity  vector  ( p1'(t), p2'(t) )\n" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "dp1 := diff(p1,t); dp2 := diff(p2,t);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 164 "\nNow we calculate the  scalar coefficie
nt   coef   such that   the pedal curve\nhas the formula\n\n       (q1
(t), q2(t)) = ( p1(t), p2(t) ) - coef*( p1'(t), p2'(t) )\n\n" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 40 "coef := (p1*dp1 + p2*dp2)/(dp1^2+dp2^2);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "Now we define the  components
 of the pedal curve position vector: \n" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 37 "q1 := p1-coef*dp1; q2 := p2-coef*dp2;" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 148 "Now we plot both the original curve and the pedal cur
ve:   Note that\nthe units must be the same on both axes --- hence the
 ``scaling=constrained''.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "plot
( \{[p1,p2,t=a..b],[q1,q2,t=a..b]\},scaling=constrained,title=`A circl
e and its pedal curve`);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 100 "\nBy
 changing the data on the first input line, one can easily draw lots o
f pedal \ncurves.   Try it.\n" }}}}{MARK "2 0 0" 0 }{VIEWOPTS 1 1 0 1 
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