# epicycloid

[ep-uh-sahy-kloid]

- 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].

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Compare epitrochoid.

## Origin of epicycloid^{}

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

## Examples from the Web for epicycloid

### Historical Examples

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

#### Suppose b a tracing point on b, then as b rolls on a it will describe the epicycloid a b.

#### It is impossible to mill out even a convex cycloid or epicycloid, by the means and in the manner above described.

#### But if a circle be made to roll along the circumference of another circle, it becomes an epicycloid (which see).

The Sailor's Word-BookWilliam Henry Smyth

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

## epicycloid

- 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 coplanarCompare hypocycloid, cycloid (def. 4)

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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

## epicycloid

[ĕp′ĭ-sī′kloid′]

- 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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The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.