Hypotrochoid: Definition from Answers.com

A hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle.

The red curve is a hypotrochoid drawn as the smaller black circle rolls around inside the larger blue circle (parameters are R = 5.0, r = 3, d = 5).

The parametric equations for a hypotrochoid are:

$x (\theta) = (R - r)\cos\theta + d\cos\left({R - r \over r}\theta\right),$

$y (\theta) = (R - r)\sin\theta - d\sin\left({R - r \over r}\theta\right).$

Special cases include the hypocycloid with d = r and the ellipse with R = 2r.

The ellipse (drawn in red) may be expressed as a special case of the hypotrochoid, with R = 2r; here R = 10, r = 5, d = 1.

The classic Spirograph toy traces out hypotrochoid and epitrochoid curves.

References

J. Dennis Lawrence (1972). A catalog of special plane curves. Dover Publications. pp. 165–168. ISBN 0-486-60288-5.

External links

Flash Animation of Hypocycloid
Hypotrochoid from Visual Dictionary of Special Plane Curves, Xah Lee.

This geometry-related article is a stub. You can help Wikipedia by expanding it.

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

Donate to Wikimedia

		Sci-Tech Dictionary. McGraw-Hill Dictionary of Scientific and Technical Terms. Copyright © 2003, 1994, 1989, 1984, 1978, 1976, 1974 by McGraw-Hill Companies, Inc. All rights reserved. Read more
		Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Hypotrochoid". Read more

Hypotrochoid

See also

References

External links