From the Greek peri "around".

 

Complex parametrization:  where a is the radius of the base circle and  that of the rolling circle (q > 1).

The pericycloids are the curves described by a point on a circle rolling without slipping on a base circle (C₀), while containing this circle.
The pericycloid with parameter q is in fact an epicycloid with parameter ; to get an epicycloid with n cusps, one has to take .
The notion of pericycloid differs from that of epicycloid only by the generation of the curve, not by the curve itself, and we refer the reader to epicycloid for a complete study.
 

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© Robert FERRÉOL 2017