Visual Sum of Squares III (proof without words)

Рет қаралды 12,326

Жыл бұрын

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 . #math #manim #mathvideo #sumofsquares #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #finitesums #discretemath
Here are three other visual proofs about the sum of squares formulas:
• Sum of Squares I (visu...
• Sum of Squares II (vis...
• A Sum of Squares Doubl...
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.
To learn more about animating with manim, check out:
manim.community
This is my version of a classic visual proof. Here are other renditions:
• Sum of n squares | exp... by ‪@ThinkTwiceLtu‬
• Sum of n square number... by ‪@Mathocube‬
• Visual Proof for Sum o... by ‪@MathPhysicsEngineering‬
___________________________________________
Music in this video:
Building The Future by MaxKoMusic | maxkomusic.com/
Music promoted by www.free-stock-music.com
Creative Commons Attribution-ShareAlike 3.0 Unported
creativecommons.org/licenses/...

Пікірлер: 39

@RandyKing314 Жыл бұрын

that was glorious. i thought for a moment the 3 pyramids would assemble to form a prism, but they are blocks not slanted 😁

@MathVisualProofs Жыл бұрын

😀

@UDHAV79 Жыл бұрын

At 1:10 I was wondering how you'd write the algebraic expression for the missing/extra squares (cubes) that would arise, and you surprised me by pulling out yet another box.😂 Loved the video :D

@MathVisualProofs Жыл бұрын

Thanks! The original static pww cuts the top triangle on half and glued it to the other side (see linked video from think twice or mathocube in the description). I like six copies of the stack better because the end result is cleaner. 😀

@lownleinhigh Жыл бұрын

Now this is clearer for me than the shorts! Haha Thank you for suggesting me this video, OP.

@MathVisualProofs Жыл бұрын

Thanks for checking it out. Shorts are hard given time constraint.

@Mutual_Information Жыл бұрын

Dude your animation skills are so good! Love this!

@MathVisualProofs Жыл бұрын

Thanks for checking it out! I get better, slowly but surely :) Always appreciate your feedback.

@monoman4083 Жыл бұрын

could watch your creations all day....

@MathVisualProofs Жыл бұрын

Thanks!

@pengin6035 Жыл бұрын

Do the n-dimensional version for the (n-1)-th powers next!

@MathVisualProofs Жыл бұрын

I'll work on it :) I do have the sum of cubes done a couple of ways on the channel, but unfortunately not one that travels to the fourth dimension...

@lloki2215 Жыл бұрын

Amazing…again.

@MathVisualProofs Жыл бұрын

Thanks!

@mrflibble5717 Жыл бұрын

Excellent, Beautiful!

@MathVisualProofs Жыл бұрын

Thank you!

@MathPhysicsEngineering 10 ай бұрын

This is exactly like my video: "Visual Proof for Sum of Squares Formula #SoME3"

@MathVisualProofs 10 ай бұрын

It’s linked in the description along with two other renditions as well. Also have the original published static diagram linked.

@DanielGutierrezC 10 ай бұрын

Beautiful!

@MathVisualProofs 10 ай бұрын

Thank you!

@DanielGutierrezC 10 ай бұрын

@@MathVisualProofs you have a new subscriber ;) I've shared this video with my students :)

@MathVisualProofs 10 ай бұрын

@@DanielGutierrezC Thanks! I hope it helps them.

@sagarnayak1000 Жыл бұрын

Tq very much for responding my previous comment and sharing this video's link.....so happy.😊👍

@MathVisualProofs Жыл бұрын

Glad you like it :)

@sagarnayak1000 Жыл бұрын

@@MathVisualProofs its not like.....i loved it...

@bobmichael8735 6 ай бұрын

could make a video about how you made those wonderful animation?please

@MathVisualProofs 6 ай бұрын

I am not sure if I know how to do that. I’ll think about it.

@naeemakhan1482 Жыл бұрын

But how _ n, n+1 and n+2 came?? Also how you use summession

@user-rw9gp6rx1m 8 ай бұрын

Stairs

@Luizabf Жыл бұрын

Maravilha

@MathVisualProofs Жыл бұрын

Thanks!

@theweebrt Жыл бұрын

They are cubes... or squares?

@MathVisualProofs Жыл бұрын

Squares of cubes

@Math_Wonders Жыл бұрын

share code?

@MathVisualProofs Жыл бұрын

I'll see what I can do. The code on these is quite a mess...

@charlesnelson5187 Жыл бұрын

Cracker!

@MathVisualProofs Жыл бұрын

😀👍