Geometric Sums of Powers of 4 @MathVisualProofs

Uploaded February 2026 | Updated September 2026, 2 weeks ago

Geometric Sums of Powers of 4

This is a short, animated (wordless) visual proof demonstrating the sums of finite geometric series of powers of 4.

This animation is based on a visual proof by David B. Sher from the Spring 1997 issue of Mathematics and Computer Education page 190.

Here’s a wide format, longer older version of this animation:
youtu.be/yTpzDEDP090

Here is a related proof for powers of 3:
youtu.be/9IAm75UY2U8

If you liked this video, consider liking or subscribing. Or you can support me by buying me a coffee at buymeacoffee.com/VisualProofs
Thanks!

#math #calculus #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricsums #series #squares #finitesums #induction #discretemath

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

Nested Powers of 2 Hypocycloids (synthwave enumeration)

Geometric sum of powers of 1/3 (v. III visual proof in a hexagon)

$Simpson’s Paradox Visually! In this short video, we show how to think about Simpsons paradox visually in terms of vector arithmetic. In particular we show that ratios can be represented by slopes of lines (or slopes of vectors) and then we can have an interesting slope reversal when adding as you would add proportions or statistics (not usual fraction arithmetic). If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! The visual proof in this video is based on a proof without words by Jerzy Kocik from the December 2001 issue of Mathematics Magazine ( https://www.jstor.org/stable/2691038 page 399). #mathshorts #mathvideo #math #statistics #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #paradox #simpsonsparadox #simpson #derekjeter #davidjustice #baseball #proportion #vectors #vectoraddition #battingaverage #data To learn more about animating with manim, check out: https://manim.community$

A Factorial Sum Produces the Factorial Number System (visual proof)

Seven Proofs Without Words for Summing Cubes