Unraveling the Area of a Circle Using the Method of Exhaustion

In this short, we show a fascinating method of determining the area of a circle using the "method of exhaustion.”

The top animation unrolls successive circumferences of nested circular shells. In this manner, the circle area gets transformed into the area of a triangle with base 2pi times r and height r.

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Here are other versions from me:
https://youtu.be/GjmtmCT5N8Q
https://youtube.com/shorts/3L_GorNnk4Q

To see an alternate (and quite viral) video showing this in stop motion, check out this one from @MinutePhysics : https://youtu.be/whYqhpc6S6g

For more information about this construction, see
https://personal.math.ubc.ca/~cass/courses/m446-03/exhaustion.pdf

or check out this nice survey article by David Richeson from the May 2015 issue of The College Math Journal: https://doi.org/10.4169/college.math.j.46.3.162 .

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To learn more about animating with manim, check out:
https://manim.community