Hypotrochoid

hypotrochoid
{1,7/13,1/13}
hypotrochoid
{1,7/13,5/13}
hypotrochoid
{1,7/13,7/13}
hypotrochoid
{1,7/13,15/13}
hypotrochoid
{1,7/5,1/13}
hypotrochoid
{1,7/5,5/13}
hypotrochoid
{1,7/5,7/13}
hypotrochoid
{1,7/5,15/13}
hypotrochoid
{1,3/4,.8/13}
hypotrochoid
{1,3/4,5/13}
hypotrochoid
{1,3/4,7/13}
hypotrochoid
{1,3/4,30/13}

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History

See epi/hypo-cycloid.

Description

Hypotrochoid describes a family of curves. Hypotrochoid and epitrochoid are roulette of two circles. If one circle is inside another, the curve traced are called hypotrochoids. Otherwise (one rolls outside another), the curves are called epitrochoids. If the tracing point is on the (circumference) rolling circle, the curves are called hypocycloid or epicycloids. Hypotrochoids are also known as SpiroGraph — a tradmark of a toy that trace limited cases of hypotrochoids. Many famous curves are special cases of hypotrochoid. (see Curve Family Index).
hypotrochoid
movie icon {1,2/3,h}
hypotrochoid
movie icon {1,2/5,1}

Formulas

See epi/hypo-cycloid.

Properties

Special Cases

Two fun movies: movie icon spiralgrap_switch.mov; spiralgraphs.mov. Mathematica icon Mathematica spiral-graph generation template

See: Websites on Plane Curves, Printed References On Plane Curves.

Robert Yates: Curves and Their Properties.

The MacTutor History of Mathematics archive↗.

© 1995-2008 by Xah Lee.
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