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# epicycloid

[ ep-*uh*-**sahy**-kloid ]

## 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*].

epicycloid

/ ˌɛpɪˈsaɪklɔɪd /

## noun

- 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

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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## Derived Forms

**ˌepicyˈcloidal**, adjective

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## Other Words From

**epi·cy·cloidal**adjective

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## Word History and Origins

Origin of epicycloid^{1}

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## Example Sentences

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

From Project Gutenberg

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

From Project Gutenberg

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

From Project Gutenberg

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

From Project Gutenberg

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

From Project Gutenberg

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