Sum Of Cubes I (visual proof)

This is a short, animated visual proof giving a formula for the sum of the first n positive cubes. #mathshorts​ #mathvideo​ #math​ #numbertheory #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #cubes #mathematics #sum

To learn more about animating with manim, check out:
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Background music, used according to CC BY-SA 3.0, is "The Road" from Esteban Orlando:

Esteban Orlando:

[benmathewson]

Great way to visually recall that sum! Thanks!

[josephmartos]

i was hoping him to say... "and thats a good place to stop" lol

[zahirgizzi]

WONDERFUL!!! Thanks for this amazing visualization! 😍

[alvarol.martinez]

Very nice once again, my opinion for future videos since I'll be watching them all: the intro feels a little long each time

[higgsbosonberg]

Beautiful. I'm always amazed by how triangle numbers turn up.

[aashsyed]

1st like, awesome work! i hope u shine and rise one day a i appreviate u a

[earthenvessels]

The final step could also have been proven visually by chopping the triangle in two vertically halfway down its length. The two shapes can then be rearranged to form a square with sides (n(n+1))/2.

[thesecondderivative]

Michael Penn sent me here. Awesome channel 👍

[saisthuvanthmadiraju]

so that means 1^3 + 2^3 + 3^3 + ... = (1+2+3+...)^2

[Manoj_b]

Is this method makes for the general sum of visual proofs

[MyNordlys]

Any visual proof existing of Basel problem ?

[nihalMaTh]

can anyone explain, how the slope is -1/2

[kales]

why does the font at the start's c look kinda weird?

[yasirsonic]

How is base n(n+1)
Why is not n.n since n is add n times

[babyineedyouinmylife]

How did you calculate the slope bro pls help

[Dunklesteus]

If you flub a line like at 0:45 on such a short video, just rerecord the audio