Areas and Perimeters of Regular Polygons (visual proof)

This is a short, animated visual proof demonstrating that the area of the regular 2n-gon inscribed in a circle of radius r is equal to one-half the product of r and the perimeter of the regular n-gon inscribed in the same circle. We finish with a bonus proof that the area of a circle is one-half the product of its radius and its circumference. #math​ #geometry #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #polygons #regularpolygon #circlearea #area #perimeter #mathshorts​ #mathvideo​

This animation is based on a visual proof by Roger B. Nelsen from his second compendium of visual proofs:

Proofs without Words I by Roger B. Nelsen (MAA, 2000) (https://bookstore.ams.org/clrm-14/)

To learn more about animating with manim, check out:
https://manim.community
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Music in this video:
Only Memories Remain by Hayden Folker |   / hayden-folker  
Music promoted by https://www.free-stock-music.com
Creative Commons Attribution 3.0 Unported License
https://creativecommons.org/licenses/...