Visual Cube Sums! (from Nicomachus)

This is a short, animated (wordless) visual proof demonstrating the sum of the first n positive cubes by rearranging cubes into a flat square.

Here are three other visual proofs of sum of cubes formulas:

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

#mathshorts​ #mathvideo​ #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #finitesums #discretemath #calculus #sum #induction

To learn more about animating with manim, check out:

[enescoskun]

The total area is (1+2+3...n)² and because (1+2+3...n) equals n²+n / 2, the formula is n²(n+1)²/4

[Bunnokazooie]

Math never gets old! Even ancient math.

[Ninja]

Its also kinda a fun prank to play. Cuz we always say (a+b)^n≠a^n+b^n, but we can say (1+2+3+…+n)^2 and “pretend” to distribute the power improperly but change the power 2 to power 3

[Mohamed-thox]

As always the best channels on YouTube are underrated and don't get enough attention😢 hidden gems

[izzabelladogalini]

I do like these videos.... most of it stuff I already know but the visual explanation is so easy to digest.... I'm a little jealous of my daughter getting to learn maths with videos like this teaching her not just rules but showing how those rules come about and so why they work for evry number .... if they don't use videos like this at her school then I'll use them at home.
Thank you for the time and effort you put into making these animations

[ThewOrldIssqUare]

How... did I never know this? I work with numbers all the time. Damn. 🤯

[anbuchelvan]

Waaw... i wondered the proof of this many tyms, here its explained as simple as possible... lovely...

[indorip]

Love the math demonstrations, keep up the posts ❤

[AlexCosta]

Beautiful video. What software do you use to animate the cubes like that?

[Blazingcharger]

So your saying that 1 plus the smallest cubed number and it doesn't work if you don't put the cubes in order and it only works with all the cube numbers between the biggest and the smallest?

[PrimordialDeity]

Hey! Can you do a visual proof for Euler's Identity?

[jonathanschmitt]

The 4 numbers lived in harmony and peace, but everything changed when the 《E》 attacked.

[algercomalekmalki]

Could this be considered as a valid mathematical proof ?

[one_logic]

I wonder if it also is true that
Σ (n^4) from 0 to ∞ = (Σ (n))^3 from 0 to ∞

[thegreatone]

Can you do an easy way to calculate pi please?

[one_logic]

The "i" you put in the bottom formulas sometimes makes me confused, as I originally think they represent √(-1)

[slutforgojosatoru]

Could you do a video on finding very large primes

[canyoupoop]

I dont like the way how even numbers are hard to break down, do you know why no. Of the form 2k behave such a way?