Self-Similar Geometric Sum in a Square: Adding Powers of 1/2 Visually! @MathVisualProofs

Uploaded April 2026 | Updated September 2026, 2 weeks ago

This is a short, animated visual proof demonstrating the infinite sum of the powers of 1/2 using 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 dissection is loosely based on a proof by Roger B. Nelsen from the February 2006 issue of Mathematics Magazine page 60. (doi.org/10.2307/27642904).

An animated version of that exact dissection is here:
youtube.com/shorts/RoovN01q83Y
or
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

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

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$Koch Curve from Binary! This video shows the first 65536 steps of the turtle graphics construction of the Koch curve using the binary sum of bits function. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! To learn more about some of the amazing properties of Thue-Morse sequence, see this longer video: https://youtu.be/yqEIhdnfJxE Or you can see Wikipedia for more: https://en.wikipedia.org/wiki/Thue%E2%80%93Morse_sequence #math #manim #kochcurve #fractal #binary To learn more about animating with manim, check out: https://manim.community$

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