Summing Powers of 1/6 via a Square Dissection @MathVisualProofs

Uploaded May 2026 | Updated September 2026, 2 weeks ago

This is a short, animated visual proof demonstrating the infinite sum of the powers of 1/6 using a square. The result is somewhat surprising given that it doesn't seem obvious how to decompose a square into powers of 1/6 and how the resulting area could easily be seen as 1/5 of a square.

If you like this video, consider subscribing to the channel or consider buying me a coffee: buymeacoffee.com/VisualProofs. Thanks!

If you like this type of video, here is my geometric sum playlist:
youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw

This animation is based on a proof by Tom Edgar from the December 2023 issue of Mathematics Magazine pages 563-565. (doi.org/10.1080/0025570X.2023.2266415 ).

#mathematics #mathvideo #math #calculus #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricseries #series #infinitesums #infiniteseries #selfsimilarity #fractal

To learn more about animating with manim, check out:
https://manim.community

$Summing Powers of 1/6 via a Square Dissection This is a short, animated visual proof demonstrating the infinite sum of the powers of 1/6 using a square. The result is somewhat surprising given that it doesnt seem obvious how to decompose a square into powers of 1/6 and how the resulting area could easily be seen as 1/5 of a square. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! If you like this type of video, here is my geometric sum playlist: https://www.youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw This animation is based on a proof by Tom Edgar from the December 2023 issue of Mathematics Magazine pages 563-565. (https://doi.org/10.1080/0025570X.2023.2266415 ). #mathematics #mathvideo #math #calculus #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricseries #series #infinitesums #infiniteseries #selfsimilarity #fractal To learn more about animating with manim, check out: https://manim.community$

$Self-Similar Geometric Series Sum Self-similar geometric series sum This is a short, animated visual proof demonstrating the infinite sum of the powers of 1/2 using a square. To see a longer version with explanation, check out: https://youtu.be/AiznRQPIwTs If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! If you like this type of video, here is my geometric sum playlist: https://www.youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw This dissection is loosely based on a proof by Roger B. Nelsen from the February 2006 issue of Mathematics Magazine page 60. (https://doi.org/10.2307/27642904). An animated version of that exact dissection is here: https://youtube.com/shorts/RoovN01q83Y or https://youtu.be/saJJGNlsfn8 #mathematics #mathvideo #math #calculus #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricseries #series #infinitesums #infiniteseries #selfsimilarity #fractal To learn more about animating with manim, check out: https://manim.community$

$Koch Snowflake: Infinite Perimeter but finite area This is a short, animation showing the Koch snowflake and discussing the fact that it has infinite perimeter but encloses a finite area. #mathshorts #mathvideo #math #fractal #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #limits #mathematics #perimeter #kochsnowflake This is a standard result that can be found in numerous places, such as Wikipedia. To learn more about animating with manim, check out: https://manim.community$