Area under a Cycloid
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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. When you slide the "roll" slider, slices form a circle of radius two times the radius of the generating circle and a circular hole as large as the generating circle. As the number of slices goes to infinity, the figure approaches a perfect cycloid (as a region) and circles. Therefore, the difference between four times the larger disk and a hole of the same size gives the area under the cycloid.
Contributed by: Okay Arik (March 2011)
Open content licensed under CC BY-NC-SA
"Area under a Cycloid"
Wolfram Demonstrations Project
Published: March 7 2011