Self Similar Geometric Series: Sums of powers of 7 (and all integers larger than 3)

Рет қаралды 6,088

Жыл бұрын

This is a short, animated visual proof demonstrating the finite geometric sum formula for any integer n with n greater than 3 (explicitly showing the cases n=7 and n=9 with k=3). This series (and its infinite analog when x less than 1) is important for many results in calculus, discrete mathematics, and combinatorics. #manim #math #geometricsums #series #calculus #mtbos #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #finitesums #finiteseries #geometric #mathshorts #mathvideo
If you like this content, please consider subscribing.
Also, check out my playlist on geometric sums/series: • Geometric Sums
This animation is based on a proof by Mingjang Chen from the December 2004 issue of Mathematics Magazine page 373 (doi.org/10.2307/3219202).
___________________________________________
Music in this video:
Epic Sci-Fi Trailer | Eternals by Alex-Productions | / @alexproductionsnocopy...
Music promoted by www.free-stock-music.com
Creative Commons Attribution 3.0 Unported License
creativecommons.org/licenses/...

Пікірлер: 31

@BariScienceLab Жыл бұрын

You’re great! Keep doing what you do. I have understood several math concepts better because of your videos!

@MathVisualProofs Жыл бұрын

Thanks!

@mathflipped Жыл бұрын

Interesting visual proof! I've never seen this kind of equality before.

@MathVisualProofs Жыл бұрын

Thanks! I love geometric sums and this way to get essentially any of the finite sums of integers was one I wanted to animate for a while.

@LorvinWolf Жыл бұрын

1:20 looks like a just shapes and beats boss

@MathVisualProofs Жыл бұрын

@symbolsforpangaea6951 Жыл бұрын

Amazing ! thank you!

@MathVisualProofs Жыл бұрын

😀

@iamtraditi4075 Жыл бұрын

gorgeous!

@MathVisualProofs Жыл бұрын

Thanks!

@MrParry1976 Жыл бұрын

Amazing! Looks almost like a fractal which makes it even more attractive!

@rishirajasekaran6055 Жыл бұрын

Yes, because it exhibits self-similarity, which is a property of fractals.

@MathVisualProofs Жыл бұрын

Yes. It essentially is a fractal! :)

@emer3376 Жыл бұрын

@@MathVisualProofs can you make a website to generate this?

@MathVisualProofs Жыл бұрын

@@emer3376 not sure I have the skills to do that.

@user-kn6sw2jl2p Жыл бұрын

WoW

@bikashchakraborty8816 Жыл бұрын

Lovely

@MathVisualProofs Жыл бұрын

Thanks as always!

@eudeciogabriel8571 Жыл бұрын

great

@MathVisualProofs Жыл бұрын

😆

@wcdeich4 Жыл бұрын

Do you have any idea how I could draw the Barnsley fern with edge lines instead of fill-in dots?

@MathVisualProofs Жыл бұрын

I don't know if I have seen a construction of Barnsley fern as an L-system or something similar. All I know is the iterated function system construction as you mention.

@Ss0oUuLl Жыл бұрын

Educational and beautiful, but music makes me think that we've just witnessed the invention of a cold fusion reactor

@MathVisualProofs Жыл бұрын

It’s that important of a formula. It drives so much mathematics that it deserves to be epically presented :)

@Nathouuuutheone Жыл бұрын

Many of your videos lack context. Any chance you can introduce what you're doing before starting your animations? It's real cute but what IS it??

@MathVisualProofs Жыл бұрын

Thanks for the feedback. Does the result at the end not reveal it?

@bikashchakraborty8816 Жыл бұрын

Hi, I love these works! These are basically proof without words, means need no explanation.

@timfieldsend816 Жыл бұрын

Unfortunately this channel's speciality is pretty pictures for university standard maths geeks. He seems unable to grasp the idea that there are some of us out here who would love to understand these concepts but don't already have the necessary grounding in the subject.