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. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! 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 . #math #manim #visualproof #proofwithoutwords #circle #circlearea #archimedes #radius #area #areaofcircle #pi #piday #shorts #circle #archimedes #infinite #methodofexhaustion To learn more about animating with manim, check out: https://manim.community