Sum of Squares I (visual proof)

This is a short, animated visual proof of the formula that computes that sum of the first n squares using 3 copies of the sum of squares to build a rectangle . #mathshorts​ #mathvideo​ #math​ #sumofsquares​ #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath
This animation is based on (independently discovered) visual proofs by Dan Kalman from the March 1991 issue of The College Mathematics Journal (www.jstor.org/...) and Martin Gardner from the October 1973 Scientific American (www.jstor.org/....
To learn more about animating with manim, check out:
manim.community
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Background music, used according to CC BY-SA 3.0, is "The Road" from Esteban Orlando:
Esteban Orlando:
/ orlando-esteba...​
/ estebanorla...​
creativecommon...
Music provided by RFM: • Video

[@aashsyed1277]

very nice thanks so much for these joyful moments!

[@MathVisualProofs]

:) I'll keep up as I can.

[@FromTheMountain]

That's a beautiful proof, nice video!

[@tomedgar9245]

Thank you. That is probably my favorite proof of this fact... though there are some other nice visual ones as well :)

[@aashsyed1277]

@@tomedgar9245 not you but micro visual proofs....

[@mahmoudalbahar1641]

Thank you very much for this cool proof

[@MathVisualProofs]

Thanks for watching! Happy you found it :)

[@CStrik3r]

Gorgeous ! What are some good sources for visual proofs like these?

[@MathVisualProofs]

Roger Nelsen is an author with many great books. He has three “Proofs without words” compendiums that are just pictures. He also has more expository books (Icons of Mathematics, Charming Proofs, When Less is More, etc) that give the reader an idea about the images and how to use them (you can read more about Nelsen’s books here : community.plu.edu/~edgartj/nelsen.pdf

[@CStrik3r]

@@MathVisualProofs Thank you so much ! Your channel is gonna be huge and help so many people with quality content right off the gates as this 🙏🏼

[@zillibran]

great stuff, the wonders of pure maths that mirrors the shapes our perpectives 👅👅keep it up.

[@jimboli9400]

Great content!

[@MathVisualProofs]

Thank you!

[@pawebielinski4903]

Extra nice!

[@MathVisualProofs]

Thank you!

[@bikalbaral1394]

awesome , this video is rare to find in you tube

[@MathVisualProofs]

Thanks! I am trying to animate some more short visual proofs.

[@HolyG-sus]

❤❤❤

[@aashsyed1277]

HELLO I DONT THINK YOU WILL BE A TOP Comenter ON THIS CHANNEL

[@samuraijosh1595]

Goddamit where were you back in the day?

[@MathVisualProofs]

happy to be here now? ;)

[@samuraijosh1595]

@@MathVisualProofs haha yeah! Keep uploading, God bless!

[@Booknotelpo]

Mathematic is My only love .

[@MathVisualProofs]

:) If there is only one, this is a good one to choose.

[@Etothetaui]

I like you other videos but this one had several very large leaps in logic. I don't really think it can be called a proof.

[@MathVisualProofs]

Thanks for the feedback. This is a classic PWW due to Dan Kalman and Martin Gardner (independently). I agree that it requires some background (that the sum of the first n positive odd integers is the nth square and the sum of the first n positive integers is n(n+1)/2). Both of the facts in the previous parenthetical statement have visual proofs (actually part of a general visual proof framework) that I hope to animate soon.