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Epicycloid--1-Cusped

Epicycloid1Cusped

A 1-cusped epicycloid has b=a, so n=1. The radius measured from the center of the large circle for a 1-cusped epicycloid is given by epicycloid equation (◇) with n=1 so

r^2=(a^2)/(n^2)[(n^2+2n+2)-2(n+1)cos(nphi)]
(1)
=a^2[(1^2+2·1+2)-2(1+1)cos(1·phi)]
(2)
=a^2(5-4cosphi)
(3)
r=asqrt(5-4cosphi),
(4)

and

tantheta=(2sinphi-sin(2phi))/(2cosphi-cos(2phi)).
(5)

The 1-cusped epicycloid is just an offset cardioid.

See also

Cardioid, Epicycloid, Nephroid

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Cite this as:

Weisstein, Eric W. "Epicycloid--1-Cusped." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Epicycloid1-Cusped.html

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