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.
#mathshorts #mathvideo #math #calculus #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricseries #series #infinitesums #infiniteseries
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. ([ Ссылка ]).
To learn more about animating with manim, check out:
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Music in the video:
The Great Battle by Alexander Nakarada | [ Ссылка ]
Music promoted by [ Ссылка ]
Attribution 4.0 International (CC BY 4.0)
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