noun Geometry.
a curve generated by the motion of a point on the circumference of a circle that rolls externally, without slipping, on a fixed circle. Equation: x = (a + b ) cos(θ) − b cos[(a + b )θ/ b ] and y = (a + b ) sin(θ) − b sin[(a + b )θ/ b ].
Compare epitrochoid.

1780–90; epicycle + -oid

epicycloidal, adjective
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World English Dictionary
epicycloid (ˌɛpɪˈsaɪklɔɪd)
hypocycloid Compare cycloid the curve described by a point on the circumference of a circle as this circle rolls around the outside of another fixed circle, the two circles being coplanar

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Science Dictionary
epicycloid   (ěp'ĭ-sī'kloid')  Pronunciation Key 
The curve described by a point on the circumference of a circle as the circle rolls on the outside of the circumference of a second, fixed circle.
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