Sums of Sums of Squares (visual proof)

This is a short, animated visual proof for the sum of the sum of squares formula using a wonderful visual proof computing the sum of squares formula.
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoff.... Thanks!
Here is a link to the visual proof for the sum of squares:
• Sum of Squares I (visu...
Here are other visual proofs about the sum of squares formulas:
• Summing Squares IV (vi...
• Visual Sum of Squares ...
• Sum of Squares II (vis...
• A Sum of Squares Doubl...
• An Amazing way to Sum ...
This animation is based on a visual proof by C.G. Wastun according to Roger Nelsen in his second Proof without Words compendium (page 91) : bookstore.ams....
This first visual proof 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:
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#math #manim​ #mathvideo​​ #sumofsquares​ #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #finitesums #discretemath #induction #sumsumsquares #partialsums

[@我不知道要叫什麼-k7r]

Next video:sums of sums of sums of squares

[@MathVisualProofs]

it’s series that will keep giving …

[@heavysaur149]

Amazing !
Such a hard looking double sum expressed easily, visually.

[@MathVisualProofs]

😀

[@average-osrs-enjoyer]

I never even realized a squared number n is just the sum of the first n odd numbers, but after doing a back-of-env induction proof now looking at (x+1)²=x²+2x+1 it makes so much sense!!!!

[@average-osrs-enjoyer]

How did I never connect these dots before hahaha 😅

[@MinhAIPet]

2:11 Best way to say f you. 😂😂😂😂😂

[@vennstudios9885]

WAIT ... ISNT THIS ... bro this looks like the silver ratio

[@MathVisualProofs]

Maybe? Haven’t thought about it yet…

[@AB-Prince]

there is a 'highscool' approch to finding the formula of a sequence, which is to write out the sequence, then write the difference of terms above, and then repeat above that until you get a constant, then use the generated sub-sequences to find the corresponding terms of the formula.

[@MathVisualProofs]

Yeah. I have a video about that on my channel (under discrete math playlist)

[@juaneosornod.9741]

I love your videos, keep doing it. what kind of book i can read about series and geometry o geometry an number theory

[@MathVisualProofs]

If you like these videos, check out books by Roger Nelsen: icons of mathematics or nuggets of number theory

[@juaneosornod.9741]

@@MathVisualProofs Thanks a lot

[@Vengemann]

Can you please try to make a visual of the basel problem sum? I sometimes can't think much about it as visual.. please

[@jakobthomsen1595]

Really good!

[@MathVisualProofs]

😀👍

[@Γιώργος-ε6τ]

Mathematicals induction is an option, takes 2 minutes to prove

[@MathVisualProofs]

But you have to know the formula first. This found and proved formulas for two different sums in 5 mins :)

[@Γιώργος-ε6τ]

@@MathVisualProofs I do not disagree. But a visual proof does not count as a proof. You could have put it in the end.

[@yb3604]

that was awesome.
kudos.

[@MathVisualProofs]

😀👍