The Amazing Cycloid Area (Visual Proof via Cavalieri)

In this video, we show how to find the area under one arch of the cycloid, which is a curve generated by tracing the path of a single point on a circle as the circle rolls on a flat surface. The cycloid area has a surprisingly nice connection to the area of the rolled circle.

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This animation is based on a visual proof by Richard M. Beekman from the February 1993 issue of Mathematics Magazine (https://www.jstor.org/stable/2690472 - page 39).


This animation is based can also be found in Roger Nelsen’s book Proofs without Words (I may receive a commission from Amazon, at no cost to you, if you click the link below):

https://amzn.to/456nvfg

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