Cut a Circle in 99 @MathVisualProofs

Uploaded August 2026 | Updated September 2026, 2 weeks ago

Cut a Circle in 99

In this short, we show how to decompose a circle into 99 pieces each with the same area. This process can be done using ruler and compass constructions. I have other videos showing why the areas are equal when you do this process for 3 parts or 7 parts. Can you figure out why these pieces all have the same area?

Here is a longer video filling the details that the seven regions are actually equal in area: youtu.be/KhfZK5IIK9E
and here is a short version of that sevenths idea:

youtube.com/shorts/2lNSnzNbAm0

Here is a video showing how to divide a line into seven equal lengths: youtu.be/afZiAGaKEY4

The same process will divide a line segment into 99 pieces 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 amzn.to/3L5U44S

maa.org/press/maa-reviews/icons-of-mathematics-an-exploration-of-twenty-key-images

bookstore.ams.org/dol-56

#manim #mathshorts #mathvideo #math #geometry #mtbos #animation #theorem #visualproof #proof #iteachmath #circle #mathematics #rulerandcompass #construction #pizza

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