Uploads from Mathematical Visual Proofs

Currently Playing: Cut a Circle in Three

Cut a Circle in Three In this short, we show how to decompose a circle into three pieces each with the same area. This process can be done using ruler and compass constructions, but is more complicated than simply constructing an inscribed equilateral triangle - but that is boring!. Here is a longer video filling the details that the seven regions are actually equal in area: https://youtu.be/KhfZK5IIK9E and here is a short version of that sevenths idea: https://youtube.com/shorts/2lNSnzNbAm0 Here is a video showing how to divide a line into seven equal lengths: https://youtu.be/afZiAGaKEY4 The same process will trisect a line segment too. 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/ #manim​ #mathshorts​ #mathvideo​ #math​ #geometry #mtbos​ #animation​ #theorem​​​ #visualproof​ #proof​ #iteachmath #circle #mathematics #rulerandcompass #construction #pizza To learn more about animating with manim, check out: https://manim.community