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.

Here is a link to the visual proof for the sum of squares:

Here are other visual proofs about the sum of squares formulas:

To learn more about animating with manim, check out:

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[我不知道要叫什麼-kr]

Next video:sums of sums of sums of squares

[heavysaur]

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

[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!!!!

[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.

[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

[vennstudios]

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

[juaneosornod.]

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

[Γιώργος-ετ]

Mathematicals induction is an option, takes 2 minutes to prove