Epicycloids I

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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An epicycloid is the curve traced by a point on the circumference of a circle as it rolls around the circumference of another circle. In this construction it's the envelope of chords across a circle, where the endpoints move but one moves faster than the other.

If there are N lobes (that is, the smaller circle rolls on a circle N times larger in diameter), then as one end of a chord steps by an angle A, the other end steps (N+1)A. If N = 1 we get a cardioid, and if N=2 we get a nephroid.

Number of lobes: Number of chords per lobe:

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Created 7 February 2012, Last Update 11 February 2012

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