Sum of n squares | explained visually |

There is a simple algebraic proof for why
1^2 + 2^2 + 3^2 +...+ n^2 = (n(n+1)(2n+1))/6 , and it's not that interesting. However I think that the visual explanation is a lot more beautiful and so I made a simple animation about it.

I know that I used only one example where n=4, but the same will work with any integer n. It's not a proof, but it will make you understand the logic behind the formula.
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Support my animations on:

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Any further questions or ideas:

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Overall render time: ~ 25 hours

Programs used:

- Cinema 4D
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Music:

Bach - Prelude in C Major

[Jabrils]

mindbending, but beautiful; the 3B1B army has arrived!

[zhengqunkoo]

Visual proofs are so intuitive. I wonder if there's a general way to prove everything visually, e.g. graphical linear algebra.

[ThinkTwiceLtu]

If you enjoyed this video please leave a like or comment below, so that more people could see it :) thank you so much

[JWentu]

I love the fact that you explained it in the time of a Bach prelude

[malingamurali]

I think it would be nicer if, instead of cutting the cubes in half and getting 1/2, to just double up that whole shape and stick it on top. Then the 2n+1 seems to come more intuitively, that's my opinion anyways haha

[omniscientomnipresent]

I am going to say it, whoever found that has a functionning brain

[LunaSuJu]

I've seen lots of other proofs but visualization is really something else. It really helps memorising things and makes formulas less intimidating. Thanks!

[hp-qxtf]

I actually shed tears of joy watching this

[yw]

your awesome dude i just spent 20 minutes scrubbing the Internet to find the source of the animations you make and god am i happy to find you

[kaziaburousan]

And here we are...the viewers of 3Blue 1Brown...what a amazing and beautiful channel it is..thanks to 3Blue 1Brown for suggesting this channel

[DarkMagek]

Commenting just due to the fact that I learnt a visual proof with beautiful music as well

[kikones]

A simple and beautiful proof. Very nice animation, good job :D!

[sunnynegi]

Wow itna simple way me proof kar diya. me khud se tricks laga ke kafi koshish ki par kuch galti ho jaati thi .Par apne to 1 minute me samjha diya

[hasiumcreeper]

I feel like putting ALL your videos in my 'Watch Later' playlist just to show to people when I'm trying to explain math.

[janschetters]

I love it. I will show it to everybody I know and not know.

[AbuTheEvil]

Thank you very much, after watching your video it's just impossible to forget the formula, and on top of it, it's not due to mere memorization but thanks to a real understanding of how it came to be. And with Bach on top of it, summing all the pleasures of the mind :)

[kennethsizer]

Excellent visualization! Excellent choice of music to accompany it! 💕

[sankarbhattacharya]

I have just seen this presentation and I can't esist writing to say how much I was carried away by it. Really it's magnificent-

[bmisawa]

I am a simple man. I see Think Twice video, I press like.

[aaronhamilton]

Holy crap! I finally understood why!! 3B1B was not mistaken in recommending you!!