Summing Squares in a Rectangle

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 .

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

To learn more about animating with manim, check out:

#mathshorts​ #mathvideo​ #math​ #sumofsquares​ #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath

[viking]

Wow, this is mind blowing my good. You guys need more views

[RenFito]

I love this visual demostration ❤
It's awesome how maths can be so interesting when you work on It!!!

[Kaviarasu_S]

I could spend all my free time swiping through shorts of Maths Visual Proofs, really great content. With love from India❤

[mananagrawal]

I only knew the 3D geometrical and the algebraic telescopic sum successive binomial expansions proof for this. I never thought of using the fact that sum of first n odd numbers is n^2 to prove this formula. Thanks!

[pctech]

I still remember this formula from my 10 th maths book

[mrisid]

I investigated the general case of representing degrees as a sum of natural numbers, and came up with a function that can test a number for prime.
Maybe we could work together.

[nibeditatripathy]

Loved your method of using geometry. ❤❤
Can you give the generalization of prime numbers ?

[mr.bastolas.]

i like your videos.
are you a student or a teacher
?

[xenonslash]

Wait can someone help explain to me the /6 to me?

[jffrysith]

no we haven't. While this works, you can't take the 4 case and say this in the n'th case for all n!

[tamirerez]

Apparently there is a limit to every good intention to explain mathematics through animation.

One millimeter after this limit, and the explanation doesn't work.

[aurnok]

Can you do 1+2⁴+3⁴+4⁴+...+n⁴ please? It will really help me ^^