Sum of Cubes Visual Proof @MathVisualProofs

Uploaded January 2025 | Updated September 2026, 2 weeks ago

This is a short, animated visual proof giving a formula for the sum of the first n positive cubes. #mathshorts #mathvideo #math #numbertheory #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #cubes #mathematics #sum

This animation is based on a visual proof by Georg Schrage from the June 1992 issue of Mathematics Magazine (doi.org/10.2307/2691330 - page 185).

To see my original wide-format version of this proof, check out
youtu.be/NxOcT_VKQR0

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

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

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