Epitrochoid

epitrochoid spiralgraph

Mathematica Notebook for This Page epitrochoid_movies.nb epitrochoid_movies2.nb

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).

epitrochoid epitrochoidGen
{1,2/3,.4}

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 .

epitrochoidLimaconGen1
{1,1,3/5}
epitrochoidCardioidGen
{1,1,1}
epitrochoidLimaconGen2
{1,1,3}

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

epitrochoidNephroidGen
{1,1/2,1/2}

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