Summing cubes with lines of squares

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

#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:

[toolebukk]

Skyrim music gave me serious chills! Nostalgia trip

[Neo-vznh]

Oh Skyrim music. You have a great taste for music.

[vladimirrodriguez]

Fantastic graphic demonstration. Please keep surprising us with your shorts.

[Ki_x]

so basically the square of the formula of triangle numbers?

[asparkdeity]

And, the RHS can be written as:

[n(n+1)/2]^2

= (1 + 2 + … + n)^2

So in fact,

1^3 + 2^3 + … + n^3 == (1 + 2 + … + n)^2


This link between the sum of cubes and the triangle numbers is extraordinary!

[jickhertz]

That's so cool wtf! I always learnt it algebraically, but this is so much more beautiful!

[gmncnr]

Geometric solution is always more understandable:)

[АлександрНовицкий-ъг]

Около месяца смотрю этот канал, как приятно осознавать универсальность математики и то что она не привязана к языку для понимания

[hydropage]

I really wonder if you could visually show that this is actually the sum of an arithmetic series squared

[AnglandAlamehnaSwedish]

Wow beautiful amazing best thing I have seen all day so sobering n clean reminds me y I was a maths major in college

[jacobhudnall-lowden]

Im still learning the multiplication tables

[partheshpunjabi]

I hope our school taught us this way.
So beautiful...

Yet I didn't understand shi*.

[mr_flor]

Why is the side "n^2+n"? I don't get it :[