Summing Squares Geometrically

This is a short, animated visual proof of the formula that computes that sum of the first n squares using 6 copies of the sum of squares pyramids to build a rectangular prism .

Here is a slower version of this video:

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

To learn more about animating with manim, check out:

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This is my version of a classic visual proof. Here are other renditions:

[estee]

I’ve read several proofs of this problem and took hours to understand them. Now I understand this in 30 seconds. So powerful

[saptadeepdeb]

It is really un expected that we can prove complex mathematical equation so beautifully by animation🔥🔥

[cmyk]

This is one of those equations that seem arbitrary and out of nowhere, but actually have a simple visual representation

[UmarFarooq_]

Many lives would have been saved if they watched this video in class.

[thelurkerbelw]

Finally, YouTube is recommending some good math

[imchillbro]

This is literally the best proof of sum of squares I've ever seen!!

[koitheawesome]

This is only the second video I've seen from this creator, and I'm already a subscriber. There is so much majesty and awe in the brilliance of the concepts they have presented to me, and the production of the videos is tops. Hella remarkable!

[Caio_Myguel]

Boy, did I struggle trying to find the formula for this expression! My approach was always geometric, but never did I think that I needed a third dimension (to "cube"), I thought I'd solve with squares and form triangles or rectangles. I didn't manage to solve it and Khan saved me with the proof. It's really good to see this animated demonstration

[kaminipatil]

Bro appeared from nowhere and cleared my struggle of couple of months in 30 sec😂

[wdyt_]

I never thought of this formula this way, but early in the beginning of the video, this construction immediately clicks in my head. Geometry is amazing!!!

[GeneralFX]

Watching your contents is fun as I love maths alotttt.. thanks for all this content and helping us understand maths even more (even though it's not in my course yet but I'll study about this very soon.. thank you ❤️)

[jackieking]

I have no idea why I watched this but that sudden ending made me gasp. Wondrous. Thank you.

[JadeDragon]

Wow, really gives you a different way of looking at it when you turn it into an actual object.

[ioerror]

The correct way to teach. Now it's so easy to grasp.

[mutatedllama]

Can't believe I learned this stuff the hard way. This just clicks instantly. You're a legend.

[AyushPal-ujwq]

i cannot find an adjective good enough to describe your explanation it is spectacular. *Subscribed*

[iainholder]

This is one of the most satisfying things I’ve ever seen

[blackpurple]

A very good visual representation of how that formula can be created

[dumnor]

summing up to n and then summing those up to n2 and then... makes nice looking series of functions.

[hamarana]

I remember having problems with mathematics because I couldn´t visualize (or didn´t have the time in school to develop a visual representation of the numbers I was learning) what was being taught. Now seeing numbers in graphic details it gives a sens of direction to go back and learn more about math!