Geometric series: sum of powers of 1/4 (visual proof)

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

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[juancristi]

I love visual proofs. I know that they can be misleading in some cases, but they are great tools to build a better intuition of math.

They show that math is not dependant on numbers, they are just a very useful representation of concepts that can be also represented geometrically. And that makes me wonder if all math cannot be reduced to geometry.

In any case, I think that it is always better to first learn math as the ancients did (visually, without using numbers or algebraic expresions) and only then, after the idea has been understood, as the moderns do (with rigorous demonstrations).

I know the pleasure of abstracting and formalizing ideas to ther most general expressions, but there is beauty in the concrete examples that is so powerful as a tool to learn and teach, that is sometimes lost in the academic environment for its own detriment.

Love your contribution of sharing your ideas and show (and cite) the ones of other great mathematicians that appreciate this angle of math.

Thanks!

[DrWeselcouch]

Nice as always! Loved the intense music!

[missingtourist]

Wordless Wednesdays are my new favorite holiday!

[mushtaqueahamed]

The binary number for 1/3 is 0.01010101... a repeating sequence of 01.

[kavyagupta]

Yesterday I encountered a question in physics that required solving this series.
I've watched this video earlier.
I didn't remembered the answer but remember that process. So I worked out on it myself, and finally I got the answer. My confidence was boosted.
THANKS FOR THESE AMAZING VIDEOS

[Grateful.For.Everything]

Very cool! Natures great spinners, the great directors of signal flow, ensuring perfect channel separation!

[SameekshaKhare-id]

Please tell me why 1-1\3 was not done in this . your teaching stylish is superb

[alexzuma.]

this is proof that you can trisect angles with straightedge and compass, it just requires infinite steps

[alexzuma.]

the sum of powers of 1/n converges to 1/(n-1)

[SameekshaKhare-id]

Please tell me why we took 1\3 of our answer and not 1-1\3 of our answer.