# Epitrochoid

Mathematica Notebook for This Page epitrochoid_movies.nb.zip epitrochoid_movies2.nb.zip

## History

See: Epicycloid and Hypocycloid.

## Description

Epitrochoid is a family of cycloidal curves, a special case of Roulette. See Epicycloid and Hypocycloid for detail. Many famous curves are special cases of epitrochoid. (See: Curve Family Index).

## Formula

See: Epicycloid and Hypocycloid.

## Properties

### Special Cases

h == 0, Circle.

b == h, epicycloids with q cusps, where q is the denominator of b written as a irreducible fraction.

a == b, limacon of Pascal. a == b == h, cardioid.

a/2 == b == h, nephroid.

### Epitrochoid and Hypotrochoid Movie Gallery

## Related Web Sites

See: Websites on Plane Curves, Plane Curves Books.

Robert Yates: Curves and Their Properties.

The MacTutor History of Mathematics archive

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