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These are some interesting
examples of algebraic curves created with GraphiCal. Please notice that GraphiCal understands expressions in cartesian as well as polar form.
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x(t)=cos(t)^3
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y(t)=sin(t)^3
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Astroid
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x(t)=2*cos(t)-cos(2*t)
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y(t)=2*sin(t)-sin(2*t)
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Cardioid
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phi(t)=t
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r(t)=a*sin(t)/t
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Cochleoid
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phi(t)=t
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r(t)=2*a*tan(t)*sin(t)
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Cissoid of Diocles
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x(t)=(a+ b)*cos(t)
-b*cos((a/b+1)*t)
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y(t)=(a+b)*sin(t)
-b*sin((a/b+1)*t)
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Epicycloid
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phi(t)=t
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r(t)= a / t
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Hyperbolic Spiral
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The expressions for the examples above were taken from
http://www-groups.dcs.st-and.ac.uk/~history/Curves/Curves.html
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