epicycloid

[ ep-uh-sahy-kloid ]

Phonetic (Standard)IPA

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 /

See cycloid, hypocycloid
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.

First recorded in 1780–90; epicycle + -oid

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.

April 18, 2024petrichor

[pet-ri-kawr]

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