Infinite Geometric Series in a Square (visual proof without words) III

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This is a short, animated visual proof demonstrating the infinite geometric series formula for any positive ratio 1-r with r less than 1 and with positive first term r. This series is important for many results in calculus, discrete mathematics, and combinatorics.
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Also, check out my playlist on geometric sums/series: • Geometric Sums
This animation is based on a proof by Warren Page from the September 1981 issue of Mathematics Magazine ( page 201 ).
#mathshorts #mathvideo #math #calculus #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricsums #series #infinitesums #infiniteseries #geometric #geometricseries
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Опубликовано:

14 окт 2024

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Комментарии : 34

@alanthayer8797 7 месяцев назад

As usual nice VISUALS to boost Assurance! Thanks

@MathVisualProofs 7 месяцев назад

Thanks!

@tsvtsvtsv 6 месяцев назад

this is a great proof, but wonder if it might have been more illustrative to show the fractal effect by varying the length of r rather than just zooming in the camera?

@MathVisualProofs 6 месяцев назад

Harder to animate but a great idea :) thanks!

@RaymondBarbour 7 месяцев назад

Had to rewatch as i missed how you showed how the long side of each rectangle was calculated. I think showing that as 1 - r - r(1 - r) would be cleared than (1 - r) - r(1 - r) Or maybe 1 - [r + r(1 - r)]

@inqurity 7 месяцев назад

Do Pi = 4 next, please!!

@MathVisualProofs 7 месяцев назад

But this one is true.

@inqurity 7 месяцев назад

@@MathVisualProofs I know, i just couldn't find a Pi = 4 "proof" without words

@MalfunctionNeo 6 месяцев назад

Except you cheated, the final square in the animation isn't black, you filled it in, there should still be a space left over however infinitesimal it is that is effectively the original square at a much smaller scale leading to a further infinite steps... This is why convergent geometric series need a Limit function to calculate, they never reach the limit, the square is never filled.

@CuriousMango247 7 месяцев назад

Shouldn't ths channel's name be 'Empirial Mathematics Proof'

@justafanoftheguywithamoust5594 7 месяцев назад

Nice name but I wouldn't say he copied it. But he rediscovered it

@CuriousMango247 7 месяцев назад

@@justafanoftheguywithamoust5594 Why? Did people not know to find finitesmal rate of change before him in the world? Is it not how Aryabhatta calculated the 24 values of sine(jya) and Madhava calculated 96 values of sine?

@CuriousMango247 7 месяцев назад

@@justafanoftheguywithamoust5594 And if you make the claim that he 'rediscovered' it, please explain why was fluxions abandoned more than a century ago? (There was nothing like fluxions existing before Newton it's just a fantasy bulls**t) You just don't want to use mathematics for its practical purposes and just want to keep yourself safe and sound in your own fantasy world!

@CuriousMango247 7 месяцев назад

@@justafanoftheguywithamoust5594 'Doctrine of Christian Discovery'🤣

@CuriousMango247 7 месяцев назад

@@justafanoftheguywithamoust5594 also Dedekind invented Dedekind cuts in 1878 Dedekind cuts and set theory(axiomatic set theory, not the cantorian set theory) is used for definition of real nos. And real nos. are used for definition of limits. So how did Newton and Leibniz 'rediscover' calculus without understanding them?