# epicycloid

[ ep-uh-sahy-kloid ]

nounGeometry.
1. 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].

## Origin of epicycloid

1
First recorded in 1780–90; epicycle + -oid

## Words Nearby epicycloid

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

## How to use epicycloid in a sentence

• The epicycloid shown is termed the “three-cusped epicycloid” or the “epicycloid of Cremona.”

• External epicycloid, described by a circle rolling about a fixed circle inside of it.

• The curve may be regarded as an epitrochoid (see epicycloid) in which the rolling and fixed circles have equal radii.

• It follows that a line from B to M will always be tangential to the epicycloid.

• Cycloid External epicycloid, described by a circle rolling about a fixed circle inside of it.

## British Dictionary definitions for epicycloid

epicycloid

/ (ˌɛpɪˈsaɪklɔɪd) /

noun
1. 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: Compare hypocycloid, cycloid (def. 4)

## Derived forms of epicycloid

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## Scientific definitions for epicycloid

epicycloid

[ ĕp′ĭ-sīkloid′ ]

1. 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.