This is a short, animated proof showing how to decompose a circle into seven pieces each with the same area. This process can be done using ruler and compass constructions, unlike the process of constructing the regular heptagon. #manim #mathshorts #mathvideo #math #geometry #mtbos #animation #theorem #visualproof #proof #iteachmath #circle #mathematics #rulerandcompass #construction #pizza
Perhaps this should be titled "The Best Way to Cut Pizza into 7 pieces" based on the comments in this video :)
There were also a number of comments asking about how to divide a line into seven equal lengths, so I have created a short, wordless animation showing that procedure if you're interested: https://youtu.be/afZiAGaKEY4
This animation is based on a visual proof from Roger Nelsen's and Claudi Alsina's wonderful book "Icons of Mathematics" (Chapter 14.1 on page 76). You can find the book and other information about it at the links below
(I may receive commissions from this paid link) : Icons of Mathematics from Amazon https://amzn.to/3L5U44S
https://www.maa.org/press/maa-reviews/icons-of-mathematics-an-exploration-of-twenty-key-images
https://bookstore.ams.org/dol-56/
To learn more about animating with manim, check out:
https://manim.community
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Music in this episode:
Divider by Chris Zabriskie is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/by/4.0/
Source: http://chriszabriskie.com/divider/
Artist: http://chriszabriskie.com/