3D Sum of Triangular Numbers (visual proof without words III)

Описание: This is a short, animated visual proof showing how to find the sum of the first n triangular numbers (which themselves are sums of the first n integers) using six three dimensional stacks of unit cubes.

If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualPr.... Thanks!

Here are some related videos with sums of triangular numbers:    • Sum of Triangular Numbers I (visual proof)  
   • Sum of Triangular Numbers II (visual proof...  
   • Geometry of the Twelve Days of X-mas (visu...  

This animation is based on a visual proof by Roger B. Nelsen from the November 1992 issue of The College Mathematics Journal (https://doi.org/10.2307/2686417 - page 417).

#manim #math #mathvideo #mathshorts #sequences #triangles #animation #theorem #pww #proofwithoutwords #visualproof #proof #triangularnumbers #sums #pww​ #proofwithoutwords​ ​ #proof​ #algebra #finitesums #mathematics​ #mathvideo​ #mtbos

To learn more about animating with manim, check out:
https://manim.community
_____________________________
Music in this video:
Heroism by MaxKoMusic | https://maxkomusic.com/
Music promoted by https://www.free-stock-music.com
Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)
https://creativecommons.org/licenses/...