Epitrochoid

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

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

History

See epi/hypo-cycloid.

Description

Epitrochoid is a family of cycloidal curves, a special case of Roulette. See epi/hypo-cycloid for detail. Many famous curves are special cases of epitrochoid. (see Curve Family Index).
{1,2/3,.4}

Formulas

See epi/hypo-cycloid

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.
  • {1,1,3/5}
  • {1,1,1}
  • {1,1,3}
• a/2 == b == h, nephroid.
  • {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.

Wikipedia: epitrochoid↗.

The MacTutor History of Mathematics archive↗.

© 1995-2008 by Xah Lee.