Five Classic Proofs without Words

In this video, we show animations of five famous/classic/iconic proofs without words: the formula for the sum of the first n integers; the formula for the difference of two squares; the formula for the sum of the first n odd integers; the pythagorean theorem using negative space/sliding rectangles/Chou pei suan ching; and the infinite geometric series of positive powers of 1/2 (using a rectangle/square dissection of a unit area square). If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! This is a longer version of this short: https://youtube.com/shorts/eG72HxNceEs?si=U2-G9e5XETuNCoth For videos with related animations, see Summing Integers: https://youtu.be/eHbtc50-qXo Pythagorean Theorem: https://youtu.be/o2mbN452ywA (and old version: https://youtu.be/yfGtbNgcrQ8) Summing Odds: https://youtu.be/I4A2T55k0cg Geometric Series: https://youtu.be/JteQEN1XPyc The first proof was known to the ancient greeks (cited by Martin Gardner), the second proof is a classic that appears in numerous places (and was likely known to Arabic mathematicians); the third is attributed to Nicomachus of Gerasa by Roger Nelsen; the fourth proof is adapted from the Chou pei suan ching (around 200 BCE according to Roger Nelsen); and the final one is attributed to Warren Page (from the September 1981 issue of Mathematics Magazine, page 201 - https://www.jstor.org/stable/2689632 ). The first three can all be found in Roger Nelsen's first compendium, "Proofs Without Words: Exercises in Visual Thinking: (I may receive a small commission at no cost to you for this affiliate link): https://amzn.to/40cQL3k https://bookstore.ams.org/view?ProductCode=CLRM/1 . #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 ______________________________ Music in this video: Flowers by FSCM Productions | https://fscmproductions.bandcamp.com Music promoted by https://www.free-stock-music.com Creative Commons / Attribution 4.0 International (CC BY 4.0) https://creativecommons.org/licenses/by/4.0/