0.66666… = 1 (in base 7)

This is a short, animated visual proof showing the sum of the infinite geometric series with first term 6/7 and ratio 1/7, which in turn allows us to compute the sum of the series of powers of 1/7 and determine an interesting base 7 representation of 1.

#mathshorts​ #mathvideo​ #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #geometricsums #series #infinitesums #infiniteseries #geometric #geometricseries #equilateraltriangle

To learn more about animating with manim, check out:

[tylosenpai]

...At this rate, you should be using a hexagon...

[mauschen_gaming]

Usually we use the formula
S = a_1 / (1 – r) but the visual proof makes it much easier to understand with the eye and I'm glad you can help others understand it more easily

[justanothergirl__]

Love this! I only wish YouTube didn't cover the bottom of the video

[h-yeum]

By reading the title, I was gobsmacked, collaterally dumbfounded and rendering my prime knowledge of math into shreds.

[kkupsky]

Omg I love these. I always was a visual learner. Numbers just are language I don’t speak. Awesome. I’ll maybe learn a bit too.

[kkupsky]

Sigma means sum? If that’s all I learned today…

[panmichael]

One can appreciate why the ancient Greeks adored geometry!

[finpin]

Love listening to these videos. I don’t learn or retain any of it but it seems pretty interesting.

[KaliFissure]

The infinite sum of a single simple fraction is the one below. 1/3+1/9+1/27... = 1/2
And 5/6+5/36+5/6³ = 1 ?
In all configurations.
So cool.

[neitoxotien]

What software do you use for animation? Thank you

[konstantindrumev]

Hi, can you please recommend any books you found useful in your journey of math? Ty❤

[Lunawithcheese]

So, polydivide (my preferred way of saying divide multiple times) by 2 and 3, then connect opposing trisectors and vertices, then connect the remaining trisectors with the midpoints, and then repeat the process with the middle triangle indefinitely, which will *precisely* give you [ *1* ]

[monie]

Surely there will always be an empty black triangle in the middle. It will never be completely filled.

[aymericd.]

All the triangle is coloured except the point in the center! No matter how many steps you do, this point will never be colored.
A non-mathematician could argue that this point is the difference between and 1.

[musicofficial]

By using infinity you can prove any number equal to any another number

[Femboy]

It's Not Art
It's Not Math

It's Both

[junhaowong]

It’s always the black magic of the concept of infinity….

[wolfscraft]

Bruh, I'm in holidays rn stop overloading my mind

[matthewbell]

This video has me all sixes and sevens

[sasho_b.]

For all sums of the type m*(1/n+1/n*n+...), the sum is equal to m*1/(n-1)