Geometric series: sum of powers of 1/3 II (visual proof)

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This is a short, animated visual proof demonstrating the infinite sum of the powers of 1/3. #mathshorts​ #mathvideo​ #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #geometricseries #series #infinitesums #infiniteseries

For an alternate series decomposition for the same series, check out

To learn more about animating with manim, check out:

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Attribution 4.0 International (CC BY 4.0)
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This is great! I like that you can convey the proof without using any speech. The music is also spot on, especially when the first third is highlighted. A suggestion: before you rotate, to show the intuition behind *why* the rotation makes for the same shape, it would be nice to show how the first vertical 1/3 corresponds to the last vertical 1/3, the first horizontal 1/3 to the last horizontal third, and so on. A curiosity: why do you use a rectangle instead of a square?

TrulyUnderstandingAlgorithms
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How would you find the partial sum formula for this series ? It obviously converges, so it would be interesting to apply the limit to check the result too, just as an exercise.

leandrodavila
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Once the picture was up I created a proof based on the fact that the zoomed in 1/9th portion of the diagram is a rotated copy of the entire diagram. Calling the sum x gives the following inductive equation: x = 4/9 + x/9 -> x = 1/2. The proof in the video is much nicer though!

amaarquadri
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Bro I don't wanna get into those cliche "😱🙀 OMG " u are so underrated stuff... Just wanna say I really hope ur channel grows considering ur contents, they are beautiful in themselves. Though it might take some time and a couple of groundbreaking contents to get ur channel's space accelerating (coz ppl these days aren't big science or math fans and on top there is this viral culture) and not everyone is luck to get noticed. Best of luck broski.

nomanbinmorshed
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Does the sum of these series always equal 1/n-1?
These are so cool to me!

doggfite