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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, ... . 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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