Summing Odds using Tokens (visual proof III)

This is a short, animated visual proof showing one method to find the sum of the first n odd positive integers by stacking tokens in a square array of cells. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! To see the other methods for finding the sum odd integers visually, check out the following videos: https://youtu.be/I4A2T55k0cg https://youtu.be/x3qfFBNRRDg https://youtu.be/ZeEOgbLo0Rg https://youtu.be/6H6nCpGW1nU For other sums related to odd integers, check out these visuals: https://youtu.be/WKxoi2i0EaE (summing odd squares) https://studio.youtube.com/video/9BC1klE8jMk/edit (alternating odd sums) https://youtu.be/MmOTqrtbtFQ (odd sum ratios) https://youtu.be/fTBvVeURb3Q (odd sum ratios II) This animation is based on a visual proof due to Timothée Duval that appeared in the Mars-Avril 2007 issue of Tangente no 115 (link. page 10). You can also find this diagram in Roger Nelsen's book on page 114: (I may receive a small commission at no cost to you for this affiliate link): https://amzn.to/47kfG7w #manim #math #mathvideo #mathshorts #sequences #triangles #animation #theorem #pww #proofwithoutwords #visualproof #proof #squarenumbers #squares #oddnumbers #odds #sums #pww​ #proofwithoutwords​ ​ #proof​ #algebra #finitesums #mathematics​ #mathvideo​ #mtbos To learn more about animating with manim, check out: https://manim.community