the following curves are special cases of the epitrochoid

Epicycloid occurs when b=c (a=5, b=c=3) |
Circle occurs when c=0 (a=5, b=3, c=0) |

Limacon of Pascal occurs when a=b (a=b=3, c=5) |
Cardioid occurs when a=b=c (a=b=c=3) |

Nephroid

occurs when a/2=b=c

(a=6, b=c=3)

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