A curve traced by a point on the circumference of a circle rolling on the exterior of another circle.
- He also investigated caustic curves and in particular he studied these associated curves of the parabola, the logarithmic spiral and epicycloids around 1692.
- The nephroid is the epicycloid formed by a circle of radius a rolling externally on a fixed circle of radius 2a.
- These are the epicycloid, the epitrochoid, the hypocycloid and the hypotrochoid and they are traced by a point P on a circle of radius b which rolls round a fixed circle of radius a.
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