> > Pedal Curves Here is an example to show how to use Maple to calculate and draw the pedal curve ( q1(t), q2(t) ) associated to a given curve ( p1(t), p2(t) ). First we supply the data for the original curve ( p1(t), p2(t) ) > p1 := cos(t)+1; p2 := sin(t); a := 0; b := 2*Pi; Now we calculate the velocity vector ( p1'(t), p2'(t) ) > dp1 := diff(p1,t); dp2 := diff(p2,t); Now we calculate the scalar coefficient coef such that the pedal curve has the formula (q1(t), q2(t)) = ( p1(t), p2(t) ) - coef*( p1'(t), p2'(t) ) > coef := (p1*dp1 + p2*dp2)/(dp1^2+dp2^2); Now we define the components of the pedal curve position vector: > q1 := p1-coef*dp1; q2 := p2-coef*dp2; Now we plot both the original curve and the pedal curve: Note that the units must be the same on both axes --- hence the ``scaling=constrained''. > plot( {[p1,p2,t=a..b],[q1,q2,t=a..b]},scaling=constrained,title=`A circle and its pedal curve`); By changing the data on the first input line, one can easily draw lots of pedal curves. Try it.