Sum of Cubes as Sum of Odds and more (visual proof VI)

This is a short, animated visual proof demonstrating two formulas for the sum of the first n positive cubes, one in terms of consecutive odd numbers and the other in terms of the square of a sum of consecutive positive integers. We end with a bonus visualization of a direct version of Nicomachus's theorem.

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

To learn more about animating with manim, check out:

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

[soumyajitroy]

Seriously a fantastic visual proof, have always been using that formula and knew the proof via mathematical induction but this is just eye opening

[RobolsMath]

Also did a video a month ago but MVP’s version is definitely better. Hoping I improve in the future. 🥹

[ryoikitokuiten]

Hi. I've discovered visual proof of the integral of tanx = ln(secx). Where can I share it with you ?