Other Definitions
hypocycloid (dict)
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HypocycloidIn geometry, a hypocycloid is a special plane curve, a roulette, generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the cycloid but instead of the circle rolling along a line, it rolls within a circle. The ratio of the radius of the larger circle to the radius of the smaller circle determines the number of cusps of the curve. For example if the ratio is 3:1 the curve will have three cusps and it will be a deltoid. Such curves can be drawn with the Spirograph toy. A hypocycloid with n + 1 cusps can be defined by the following pair of parametric equations: -
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The hypocycloid is a special kind of hypotrochoid. A hypocycloid and its evolute are similar.http://mathworld.wolfram.com/HypocycloidEvolute.html A hypocycloid curve with four cusps is known as an astroid. See also: cycloid, epicycloid.
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