Top four visual proofs?

In this short, we show animations of four of the most famous proofs without words: the formula for the sum of the first n integers; the pythagorean theorem using negative space/sliding rectangles/Chou pei suan ching; the formula for the sum of the first n odd integers; and the infinite geometric series of positive powers of 1/2 (using a rectangle/square dissection of a unit area square). We include brief justifications for these visual proofs.

For a slightly different version of this short without words, see:

For longer videos with related animations, see

#math #manim #pythagoreantheorem #pythagorean #triangle #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo #geometricseries #infiniteseries #finitesums #infinitesums #oddsumformula #sumsofintegers #sums #shorts

To learn more about animating with manim, check out:

[RunstarHomer]

"proofs without words"
*continues talking*

Just kidding, cool video :)

[algebraic_combinatorist]

This channel is mega underrated … should blow up
Visual proofs with infinity are always kinda fishy. I wouldn’t rely on those. Other three are fantastic. Can you do one for summation of n^3 ?

[anuragrebelli]

Have to remember the mathematician Gauss who invented the proof for sum of n natural numbers when he's in school!! 😱🥶🧠

[Fangamer]

1st equation I found them myself bc I wanted to shorten time to calculate infinite sums.
Then I've realized that wait if we cut a square in half & we add x cut in half again we get (x^2 +x)/2

[average-osrs-enjoyer]

The first and last one I figured out myself when facef with the series before when I was younger, but I never saw the middle two before, neat! Thanks!

[primenumber]

It is awesome!!! How do you make it? Can you share me what tools you use?

[mythicknight]

Man i barely understand this right away but its cool

[ThePatify]

Mathologer has an awesome visual proof that ln is primitive of 1/x

[tim_exp]

1 is also an infinity. Some infinities are greater than others or at least represent a difference.

[realitant]

You should do sum of cubes = square of sum of natural numbers

[CarlJohnson-mizo]

Isn't the last one (1/2)^n series? And that is a geometric series that would converge to 2

[mathcraft]

1+2+3…+n=
n…+1
Add them
Divide by 2 (cuz u did it twice)

[rezah]

we engineers never need this, it's nice maths but proofs are useless, just puzzle games

[ethanbartiromo]

I hope everyone watching this channel knows that these are used to make it easy to learn, but they are not actually sufficient as a proof. Pictures and diagrams are not proofs, if you use a diagram to explain, then it must be able to display all values of n for any positive integer n, unless you use induction

[FxFezzy]

Can you make a visual proof for 1/n^2=pi^2/6

[JesusPlsSaveMe]

Math is truly incredible


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