Uploaded February 2026 | Updated September 2026, 2 weeks ago

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Summing Odds via Perspective Change

In this short animation, we show how to find the sum of the first n odd positive integers just by changing your perspective in 3D space.

This animation is based on a beautiful animated gif created by Vincent Pantaloni:

geogebra.org/resource/qhn8mapb/obNkpO71wSptOApW/material-qhn8mapb.gif

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Thanks!


#manim #finitesum #proofwithoutwords #mathematics #numbertheory #mathvideo​ #math​ #mtbos​ ​ #perspective #induction

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