Alternating Geometric Series (ratio 1/2) @MathVisualProofs

Uploaded December 2025 | Updated September 2026, 2 weeks ago

This is a short, animated (wordless) visual proof demonstrating the sum of the infinite geometric series with ratio -1/2.

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This animation is based on a visual proof by Ángel Plaza from the May 2018 issue of The College Math Journal page 200 (doi.org/10.1080/07468342.2018.1437302).

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$Alternating Geometric Series (ratio 1/2) This is a short, animated (wordless) visual proof demonstrating the sum of the infinite geometric series with ratio -1/2. To buy me a coffee, head over to https://www.buymeacoffee.com/VisualProofs Thanks! This animation is based on a visual proof by Ángel Plaza from the May 2018 issue of The College Math Journal page 200 (https://doi.org/10.1080/07468342.2018.1437302). #mathshorts #mathvideo #math #calculus #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricseries #infiniteseries #fractals #sum #induction To learn more about animating with manim, check out: https://manim.community$

$Chaos in a Heptagon! In this short, we show what happens when iterating the procedure of choosing a heptagon vertex at random and moving 0.692 of the distance from the current dot to the chosen point. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! If you want to know more about the Chaos game, see the following links: https://en.wikipedia.org/wiki/Chaos_game https://mathworld.wolfram.com/ChaosGa... https://math.bu.edu/DYSYS/chaos-game/... https://youtu.be/kbKtFN71Lfs https://youtu.be/IGlGvSXkRGI https://youtube.com/shorts/yDHkNDrHfIw #chaos #chaosgame #heptagon #mathvideo #math #mtbos #manim #animation #theorem #iteachmath #mathematics #dynamicalsystems #iteratedfunctionsystem #dynamics #fractal #fractals To learn more about animating with manim, check out: https://manim.community$

$Mediant Inequality from Slopes This is a short, animated visual proof demonstrating what one might call the mediant inequality. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! For an alternate visual proof of this fact, see: https://youtu.be/RKeBuWL1B4A https://youtube.com/shorts/cI92ZID95g4 https://youtu.be/pODylgdI3p8 For the wide format of this video, see: https://youtu.be/AuxqpiDTCyU?si=kLa0Un4L8ADM6a_q This animation is based on a visual proof by Li Changming from the January 1988 issue of Mathematics Teacher (https://www.jstor.org/stable/27965677 - page 63). #math #inequality #numbertheory #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #fractions #mediant #mathematics #fareyfractions #farey #mathshorts #mathvideo To learn more about animating with manim, check out: https://manim.community$

Mathematical Visual Proofs |

Alternating Geometric Series (ratio =-1/2)