Two Nonstandard Infinite Geometric Series (visual proof)

Описание: My previous wordless Wednesday video showing the sum of the powers of 1/7 generated some interesting questions about using the same technique for nonstandard geometric series. Here we include a short, animated visual proof demonstrating the infinite sum of the powers of 2/7 and 3/11; from these dissections, you should be able to generate a similar circular diagram for any rational number ratio r=a/b where the infinite sum will be between 0 and 1. These two series were explicitly mentioned by James Tanton and Dr. Barker.
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This animation was inspired by comments in a a proof by James Tanton from the March 2008 issue of The College Mathematics Journal page 106. (https://www.jstor.org/stable/27646594).

To learn more about animating with manim, check out:
https://manim.community
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Music in the video:
The Great Battle by Alexander Nakarada | https://www.serpentsoundstudios.com
Music promoted by https://www.free-stock-music.com
Attribution 4.0 International (CC BY 4.0)
https://creativecommons.org/licenses/...