Area under a Cycloid (II)

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This Demonstration shows that the area under the first hump of a cycloid is three times the area of its generating circle. The "flip" slider places slices in reverse order. The "align" slider slides slices over each other and forms two unit circles. As the number of slices goes to infinity, the figure approaches a perfect cycloid (as a region) and circles. Therefore, the area of three unit circles gives the area under the cycloid.

Contributed by: Okay Arik (January 2012)
Open content licensed under CC BY-NC-SA


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