Summing Powers of 5 @MathVisualProofs

Uploaded June 2026 | Updated September 2026, 2 weeks ago

Summing Powers of 5

This is a short, animated visual proof demonstrating the finite geometric sum formula for any integer n with n greater than 3 (explicitly showing the case n=5 with k=3). This series (and its infinite analog when x less than 1) is important for many results in calculus, discrete mathematics, and combinatorics.

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For a longer version of this video with other geometric sums (to see how this generalizes), check out: youtu.be/1wIdJxSfUz4

Also, check out my playlist on geometric sums/series: youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw

This animation is based on a proof by Mingjang Chen from the December 2004 issue of Mathematics Magazine page 373 (doi.org/10.2307/3219202).

#manim #math #geometricsums #series #proofwithoutwords

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$Hilbert Curve from an L System In this video, we describe two how to draw a plane filling curve called the Hilbert curve using an L-system. While the substitution strings are a bit complicated, the rules for this system are easy to implement and use to draw a level 8 Hilbert curve (to dramatic music). If you liked this video, consider liking or subscribing. Or you can support me by buying me a coffee at https://www.buymeacoffee.com/VisualProofs Thanks! If you want to see other constructions of like this, see https://youtu.be/GVhLhAXAWoI https://youtu.be/MEzgGGq2l5E https://youtu.be/8Q_zuRKKh2g https://youtu.be/UKNcbNpP w If you want to know more about L-systems or turtle graphics or the Gosper curve, check out these wikipedia sites: https://en.wikipedia.org/wiki/L-system https://en.wikipedia.org/wiki/Turtle_graphics https://en.wikipedia.org/wiki/Hilbert_curve To learn more about animating with manim, check out: https://manim.community #turtlegraphics #fractal #math #manim #mathvideo #Lsystem #hilbert #hilbertcurve #planefillingcurve #visualmath #fractalcurves Music in this video: Voyager by Alex-Productions | https://onsound.eu/ Music promoted by https://www.free-stock-music.com Creative Commons / Attribution 3.0 Unported License (CC BY 3.0) https://creativecommons.org/licenses/by/3.0/deed.en_US$

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