Hypotrochoid
From Wikipedia, the free encyclopedia
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:
Special cases include the hypocycloid with d = r and the ellipse with R = 2r.
The classic Spirograph toy traces out hypotrochoid and epitrochoid curves.
[edit] See also
- epitrochoid
- Spirograph (toy)
[edit] External links
- Flash Animation of Hypocycloid
- Hypotrochoid from Visual Dictionary of Special Plane Curves, Xah Lee.
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