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: [ Ссылка ]
Level 2, Tokens on Triangular Array: [ Ссылка ]
Level 3, Rectangular Dissection: [ Ссылка ]
Level 4, Pyramidal Stacks: [ Ссылка ]
Level 5, Stacking Cuboids: [ Ссылка ]
You can see short versions of a levels 3 and 4 here:
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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 ([ Ссылка ] ).
Level 2: This animation is based on a visual proof by Sidney H. Kung from the May 1989 issue of The College Mathematics Journal ([ Ссылка ]) 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 ([ Ссылка ]) and Martin Gardner from the October 1973 Scientific American ([ Ссылка ]).
Level 4: This animation is based on a visual proof by Man-Keung Siu from the March 1984 issue of Mathematics Magazine ([ Ссылка ]), page 92.
Level 5: This animation is based on a visual proof by Sasho Kalajdzievski from the June 2000 issue of The Mathematical Intelligencer ([ Ссылка ] pages 47--49 ).
#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:
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