This is a short, animated visual proof showing the sum of the infinite geometric series of powers of 1/8 (starting with 1/8) is 1/7 using self similar trapezoids in a regular heptagon. #manim #math #mathshorts #mathvideo #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #calculus #series #geometricseries #infiniteseries #heptagon #trapezoids
Here is an alternate dissection proof for this series: [ Ссылка ]
Here is a longer form video with lots of related infinite geometric sums: [ Ссылка ]
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This animation is based on 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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