Curves62 of 113

Epicycloid

Hipparchus, 2nd century BC; Albrecht Dürer, 1525

The path of a point on the rim of a wheel that rolls round the outside of a fixed circle. When the ratio of the radii is a fraction n/d in lowest terms the curve has n cusps, and when d is more than 1 its arches cross. The cardioid is the case of one cusp and the nephroid of two.

x = (R + r) cos θ - r cos((R + r)θ/r), y = (R + r) sin θ - r sin((R + r)θ/r)

On mathcurve.com as Épicycloïde

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