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Curated by: Mathematical Visual Proofs (650 videos)
Four Nonstandard Visual Proofs of Classic Facts In this short, we show animations of four nonstandard visual proofs of famous facts with much more standard proofs without words: the formula for the sum of the first n integers using 8 staircase stacks; the pythagorean theorem using scaling; the formula for the sum of the first n odd integers using 4 triangular-ish stacks; and the infinite geometric series of positive powers of 1/10 (using a nonagon dissection proof), which also shows that 0.999.... = 1. We include brief justifications for these visual proofs. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! For videos with the classic visual proofs see: https://youtube.com/shorts/eG72HxNceEs or https://youtube.com/shorts/gnGxF0XcGZ8 For videos with related animations, see Summing Integers: https://youtu.be/8Jco4DfK6D0 Pythagorean Theorem: https://youtu.be/q28H5NY5UVU or https://youtube.com/shorts/1gFB7dG_t00 Summing Odds: https://youtu.be/ZeEOgbLo0Rg or https://youtube.com/shorts/G1JrE3875M8 Geometric Series: https://youtu.be/BGsJjHbjcnA or https://youtube.com/shorts/Gi0GAaw-bb4 The summing integers proof is based on a visual proof by Edwin G. Landauer from the September 1985 issue of Mathematics Magazine (https://www.jstor.org/stable/2689514 - page 203). The Pythagorean theorem proof is based on a visual proof by Frank Burk from the November 1996 issue of The College Mathematics Journal (https://doi.org/10.2307/2687335 page 409). The sum of odds proof is based on a visual proof by Roger B. Nelsen from his first compendium of visual proofs: Proofs without Words I by Roger B. Nelsen (MAA, 1993) (https://bookstore.ams.org/clrm-1) The geometric series (0.999...=1) proof is based on a proof by James Tanton ( @JamesTantonMath ) the March 2008 issue of The College Mathematics Journal page 106. (https://www.jstor.org/stable/27646594 ). #math #manim #pythagoreantheorem #pythagorean #triangle #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo #geometricseries #infiniteseries #finitesums #infinitesums #oddsumformula #sumsofintegers #sums #shorts To learn more about animating with manim, check out: https://manim.community