This video is a compilation of five different visual proofs showing the sum formula for the sum of the first n positive squares that can be found on my channel. This is a new style of video for me inspired by  @ThatsAmazing 's trick shots at various levels and  @dudeperfect 's soundtracks. I hope you enjoy it. These visual proofs are likely too fast to follow completely in this format, so the originals are linked below.

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For the original animations, see here:
Level 1, Induction Dissection:    • Summing Squares IV (visual proof with...  
Level 2, Tokens on Triangular Array:    • Sum of Squares II (visual proof)  
Level 3, Rectangular Dissection:    • Sum of Squares I (visual proof)  
Level 4, Pyramidal Stacks:    • Visual Sum of Squares III (proof with...  
Level 5, Stacking Cuboids:    • An Amazing way to Sum Squares (visual...  

You can see short versions of a levels 3 and 4 here:
   • Summing Squares in a Rectangle  
   • Summing Squares Geometrically  

Original sources:
Level 1: This animation is based on a visual proof by Tom Edgar from the International Journal of Mathematical Education in Science and Technology (https://doi.org/10.1080/0020739X.2022... ).
Level 2: This animation is based on a visual proof by Sidney H. Kung from the May 1989 issue of The College Mathematics Journal (https://doi.org/10.2307/2686767) page 205.
Level 3: This animation is based on (independently discovered) visual proofs by Dan Kalman from the March 1991 issue of The College Mathematics Journal (https://www.jstor.org/stable/2686447) and Martin Gardner from the October 1973 Scientific American (https://www.jstor.org/stable/24923225).
Level 4: This animation is based on a visual proof by ManKeung Siu from the March 1984 issue of Mathematics Magazine (https://www.jstor.org/stable/2689589), page 92.
Level 5: This animation is based on a visual proof by Sasho Kalajdzievski from the June 2000 issue of The Mathematical Intelligencer (https://doi.org/10.1007/BF03025282 pages 4749 ).

#math #manim​ #mathvideo​​ #sumofsquares​ #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #finitesums #discretemath #induction

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