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Curated by: Mathematical Visual Proofs (650 videos)
Arithmetico-Geometric Series via Gabriel’s Staircase This is a short, animated visual proof computing the sum of the differentiated geometric series with terms of the form k times r^k where r is between 0 and 1. The proof uses a fascinating object called Gabriel's staircase, which has infinite perimeter but encloses a finite area. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks This animation is based on a visual proof by Stuart G. Swain from the June 1994 issue of Mathematics Magazine (https://doi.org/10.2307/2690612 p. 209). #math #infiniteseries #manim #visualproof #geometricseries To learn more about animating with manim, check out: https://manim.community