Скачать или смотреть Visual Algebraic Identities: A Tour de Force

In this video, we compile some of the best visual proofs of algebraic identities. Using the area model can help us remember certain algebraic identities by remembering the associated images.

Note : Sodorack noticed a typo in first list of equations at 11 seconds in. The completing the square formula has a “+c” on the left. That should still be there on the right. Thanks!


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

1) Distributive Law and Foil:    • Don't use FOIL! (distributive property are...  
2) Square of a sum (classic; I don't know the original attribution)
3) Cube of a sum (classic; I don't know the original attribution)
4) Complete the Square and Quadratic Formula (This animation is based on a visual proof due to Charles D. Gallant from the March 1983 issue of Mathematics Magazine: https://www.jstor.org/stable/2690382 (page 110)) :    • Quadratic Formula Visually!  
5) Difference of Cubes (classic; I don't know an original source):    • Factor a Difference of Two Cubes! (visual ...  
6) Sum of Cubes (classic; I don't know an original source) :    • Factor a Sum of Two Cubes (visual proof wi...  
7) Difference of squares (This animation is based on a visual proof by Munir Mahmood from the January 2014 issue of The College Mathematics Journal (https://doi.org/10.4169/college.math.... ) page 21.) :    • Completing The Square via the Difference o...  
8) AM/GM from Square ( This animation is based on a visual proof by Doris Schattschneider from the February 1986 issue of Mathematics Magazine (https://doi.org/10.2307/2690011 ) ) :    • Visual Proof of AM-GM Inequality I   and    • AM-GM inequality visually  
9) AM/RMS from to Squares ( This animation is based on a visual proof by Shirly Wakin from the September 1984 issue of Mathematics Magazine (https://doi.org/10.2307/2689683 - page 231). ) :    • An Algebraic Areas Identity (visual proof)  
10) Candido's Identity ( This animation is based on a visual proof by Roger B. Nelsen from the April 2005 issue of Mathematics Magazine (https://doi.org/10.2307/30044141 - page 131). ) :    • Candido's Identity (visual animated proof ...  


Also, check out my playlist of algebra:    • Algebra  


#mathvideo​ #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #algebra #visualidentities #identities #algebraicreasoning #highschoolmath #candido #squares #square #area #areas #distributiveproperty #distribution #inequality #amgminequality #arithmeticmean #geometricmean #rootmeansquare #some4 #SoME4

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