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# epicycloid

[ep-uh-sahy-kloid]
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noun Geometry.
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].
Compare epitrochoid.

## Origin of .css-1fxfie5{font-size:22px;}@media (max-width:768px){.css-1fxfie5{font-size:18px;margin:0 10px 10px 0;word-break:break-all;word-wrap:break-word;-webkit-hyphens:auto;-moz-hyphens:auto;-ms-hyphens:auto;hyphens:auto;line-height:22px;}}epicycloid

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

Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 5

Various

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

The Sailor's Word-Book

William Henry Smyth

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

British Dictionary definitions for epicycloid

# epicycloid

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 coplanarCompare hypocycloid, cycloid (def. 4)