Area of Epicycloid and Hypocycloid

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This Demonstration shows that the area under the first hump of a epicycloid is when the radii of the generating circle and greater circle are and respectively. When you slide the "roll" slider, slices form a circle of radius and a circular hole of radius . Therefore the area is the difference of areas of the two circles. In other words, .

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For the hypocycloid, the same result holds with negative.

As the number of slices goes to infinity, the dark figure approaches a region bounded by a perfect epicycloid or hypocycloid.

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Contributed by: Okay Arik (March 2011)
Open content licensed under CC BY-NC-SA


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