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Topic: Hypotrochoid

	Hypotrochoid
		These are the epicycloid, the epitrochoid, the hypocycloid and the hypotrochoid and they are traced by a point P on a circle of radius b which rolls round a fixed circle of radius a.
		For the hypotrochoid, an example of which is shown above, the circle of radius b rolls on the inside of the circle of radius a.
		The point P is at distance c from the centre of the circle of radius b.
	www-groups.dcs.st-and.ac.uk /~history/Curves/Hypotrochoid.html (157 words)

	Encyclopedia: Hypotrochoid (Site not responding. Last check: )
		The parametric equations for a hypotrochoid are: Graph of a butterfly curve, a parametric equation discovered by Temple H. Fay In mathematics, a parametric equation explicitly relates two or more variables in terms of one or more independent parameters.
		Special cases include the hypocycloid with d = r and the ellipse with R = 2r In 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.
		Finally, the hypotrochoid is a specific case of the cycloidal curves in which both the fixed curve and the rolling curve are circles and the rolling circle is rolling against the inside of the fixed curve without slippage.
	www.nationmaster.com /encyclopedia/Hypotrochoid (493 words)

	hypotrochoid
		A curve formed by the path of a point attached to a point c, which is not on the circumference, of circle of radius b that rolls around the inside of a larger circle of radius a.
		The hypotrochoid is a generalized hypocycloid and comes in two varieties: a prolate hypocycloid if the starting point is outside the circumference of the rolling circle and a curtate hypocycloid if the starting point is inside the rolling circle.
		In the same family of curves as the hypotrochoid (and hypocycloid) are the epicycloid and epitrochoid.
	www.daviddarling.info /encyclopedia/H/hypotrochoid.html (202 words)

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