Sum of Squares Visual Proofs: From Level 1 to Level 5

This video is a compilation of five different visual proofs showing the sum formula for the sum of the first n positive squares that can be found on my channel. This is a new style of video for me inspired by @ThatsAmazing 's trick shots at various levels and @dudeperfect 's soundtracks. I hope you enjoy it. These visual proofs are likely too fast to follow completely in this format, so the originals are linked below.
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoffee.com/VisualPr.... Thanks!
For the original animations, see here:
Level 1, Induction Dissection: • Summing Squares IV (vi...
Level 2, Tokens on Triangular Array: • Sum of Squares II (vis...
Level 3, Rectangular Dissection: • Sum of Squares I (visu...
Level 4, Pyramidal Stacks: • Visual Sum of Squares ...
Level 5, Stacking Cuboids: • An Amazing way to Sum ...
You can see short versions of a levels 3 and 4 here:
• Summing Squares in a R...
• Summing Squares Geomet...
Original sources:
Level 1: This animation is based on a visual proof by Tom Edgar from the International Journal of Mathematical Education in Science and Technology (doi.org/10.1080/0020739X.2022... ).
Level 2: This animation is based on a visual proof by Sidney H. Kung from the May 1989 issue of The College Mathematics Journal (doi.org/10.2307/2686767) page 205.
Level 3: This animation is based on (independently discovered) visual proofs by Dan Kalman from the March 1991 issue of The College Mathematics Journal (www.jstor.org/stable/2686447) and Martin Gardner from the October 1973 Scientific American (www.jstor.org/stable/24923225).
Level 4: This animation is based on a visual proof by Man-Keung Siu from the March 1984 issue of Mathematics Magazine (www.jstor.org/stable/2689589), page 92.
Level 5: This animation is based on a visual proof by Sasho Kalajdzievski from the June 2000 issue of The Mathematical Intelligencer (doi.org/10.1007/BF03025282 pages 47--49 ).
#math #manim​ #mathvideo​​ #sumofsquares​ #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #finitesums #discretemath #induction
To learn more about animating with manim, check out:
manim.community

[@hugominecraft7470]

The background song reminded me of a dude perfect video!!!!! 😂😂😂
Nice work ❤❤

[@MathVisualProofs]

Thanks! It was definitely inspired by dude perfect style vids :)

[@Axenvyy]

Second Proof wins my heart!

[@quiptheip]

I only came across your channel recently and I’m addicted 😅
Each one has a really nice charm, is hard to pick one out specifically 🙂

[@MathVisualProofs]

Thanks for watching them! And welcome to the channel! :)

[@arnavsingh9374]

​@@MathVisualProofs Same here

[@jimmy_4]

the second proof deserves the first place
i wonder how people come up with these genius thoughts👏👏👏👏

[@DaReelGamerz]

Second proof is the best in my perspective by far

[@MathVisualProofs]

I like 3 best :)

[@anyoung1818]

Dude this video is perfect!

[@1729andres]

Beautiful as always. One of the best videos of your channel, thank you!

[@MathVisualProofs]

Wow, thank you!

[@Iammuslimaakter]

I wish I had seen this when I was trying so hard to memorize it in 9th grade.

[@horlickminton6534]

Love it

[@sundareshvenugopal6575]

Good channel. Good work.

[@MathVisualProofs]

Thanks!

[@sumeru0728]

your work is amazing 👏 👏 👏

[@MathVisualProofs]

Thanks!

[@ntombi105]

Pyramidal stacks were my fave

[@MathVisualProofs]

👍😀

[@techbricks7539]

I loved the sushi ones 😂

[@MathVisualProofs]

👍

[@tyroneshareef3619]

Damn, you did it dog!

[@xen_relay2]

my math is mathing

[@missingtourist3746]

🤘🔥

[@MathVisualProofs]

😎

[@doyalbatra]

I cant understand how we are getting 2n +1 for each triangle in the second level, i understood the derivation of 2n+1 in the top triangle of the three traingles, im not able to get it ahead

[@goosemchonk]

I didn't understand any of these until level 5 for some reason

[@proxyprox]

5 was indeed the best one

[@MathVisualProofs]

Hmm. I find 5 takes the most thought to believe all the cuboids fit right. Just me though :) I find most people like 4 the best. But I’m particularly fond of 3.

[@GeneralFX]

Can you make a video on teaching us Derivative, limits and differentiation... I'm from India and in 11th grade and we have a chapter limits and derivatives... And I'm officially having a hard time understanding this topic...

[@MathVisualProofs]

Check out 3blue1brown essence of calculus. I won’t be able to do it better.

[@saurabhnegi9636]

​@@MathVisualProofs
Wow!
Ur humility shows how much u care for Audience.

[@Fire_Axus]

unconvincing

[@MathVisualProofs]

Not one level?

[@GaborRevesz_kittenhuffer]

nice vid, but the music is so obnoxious i had to mute it

[@MathVisualProofs]

Hah! It’s not trick shot inspired without it :) links to originals in the description - but not sure you’ll like that music either :)