A visual infinite sum like you’ve never seen!

This is a short, animated visual proof demonstrating the sum of the infinite series of the powers of 1/4. #shorts​​ #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #geometricseries #series #infiniteseries #fractal

To learn more about animating with manim, check out:

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[anjalidwivedi]

This is the best visual proof of a series I've ever seen.. underrated 😊😊

[ok.]

Man, why is this channel so underrated🙌

[derivalz]

Look them horizontally and note that 1/3 is shaded and 2/3 is unshaded thus your end result if you go on infinite times

[MV-vvsg]

Love how we made number and geometry align so well that we can use each to prove another. Picture is just as important to human learning as propositional signs. In this case it’s wonderful how the visual proof can do more than what equation manipulation / iterative summing can do.

[alexandrudanciu]

First time seeing this, but you're so talented at explaining = subscribed straight away!

[sakshamsrivastava]

That's so amazing, you just got another subscriber

[AppleHeinz]

This is just visually stunning. It is so calming to watch these videos thanks to the graphics artist.

[radhakrishnamohanty]

You got a new subscriber for this video.

[siddhesh]

Wow you never run out of these amazing visual proofs
Amazing as always.

[amv]

I never understood infinite sums as a student. These videos make them so intuitive!

[tonitalas]

Best visual I have ever seen for infinite series! Thank you 😊

[machobunny]

I've been wondering about that for decades. Thanks so much.

[redcrewmate]

1. Split the top part into fourths
2. Color 1/4
3. Ignore the top part; area is 1/3
Repeat forever

[dipanshuagrawal]

Subscribed hope you provide more such videos, BYJU'S like learning

[Andrej.....]

Love youe videos! Keep up the good work!

[kartik-mwvs]

I can binge watch this type of content u deserve a million subscriber❤

[abdelkarimdebbah]

I figured it out correctly on my own!!! I've really learned something valuable from this! I'm really grateful!

[vintage_osu]

Damn... that's nuts, math is always so pretty and has like almost an artistical beauty to it, I love it

[theAmazingJunkman]

I actually learned about this in the game Factorio. Long story short, I needed a way to divide a bunch of items into 3 equal groups, but I could only divide by powers of 2. The solution was divide the input by 4, send 3 of the 4 groups out as output, then run the 4th group back in as input, repeat until all the items are divided 3 ways.

[Cryp_Crid]

For people struggling, try imagining the same process where the middle triangle is a scaled down version of the original not a rotation, where it is 1/4 of the original, connect the corners of the smaller triangle with those of the bigger one, do it infinitely
And you end up with 3 triangles