Epitrochoid

epitrochoid
{1,1/5,.1}
epitrochoid
{1,1/5,.6}
epitrochoid
{1,1/5,1.2}
epitrochoid
{1,1/5,2.6}
epitrochoid
{1,2/5,.1}
epitrochoid
{1,2/5,.6}
epitrochoid
{1,2/5,1.2}
epitrochoid
{1,2/5,2.6}
epitrochoid
{1,3/5,.1}
epitrochoid
{1,3/5,.6}
epitrochoid
{1,3/5,1.2}
epitrochoid
{1,3/5,2.6}
epitrochoid
{1,4/5,.1}
epitrochoid
{1,4/5,.6}
epitrochoid
{1,4/5,1.2}
epitrochoid
{1,4/5,2.6}

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

History

Differential Equations, Mechanics, and Computation

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}

Formulas

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, Printed References On Plane Curves.

Robert Yates: Curves and Their Properties.

The MacTutor History of Mathematics archive

blog comments powered by Disqus