Beautiful Geometry behind Geometric Series (8 dissection visual proofs without words) #math #series

This video is a compilation of eight shorter videos I have created showing dissection proofs for infinite geometric series with ratio of the form 1/n and first term 1/n. To see the original videos (in shorter form and typically with more dramatic music), check the links below. When you have seen enough of these dissections, you should be able to guess the general formula for such a geometric series (and perhaps the more general form, which can be found in other videos on my channel).

Here are the original series videos (along with attribution; for more detailed attribution, see the original videos):

If you like series dissections, check out my playlists:

#manim #math​​ #mathshorts​ #mathvideo​ #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #calculus #series #geometricseries #infiniteseries #dissection #dissectionproof #geometricsum #sums #calculus2

To learn more about animating with manim, check out:
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Music:
Attribution 4.0 International (CC BY 4.0)

[Psychospheres]

I never really liked math as a teen and I'm just now starting my journey into mathematics and things like this make me really appreciate beauty in it. Excellent job.

[sleha]

If math is an art, you are no less than Vinc. These were so peaceful, elegant and true pieces of beauty

[pauldokter]

Oh, sweet. Gave me chills. Makes me wish I were a kid again starting out fresh on math explorations. Thank you.

[louigomes]

I have seen the majority of them on olympics or challenges, and i finally discovering that it has some logix behind, the point that it isn't just uses to be in a random question, but the beauty of geometry.

[yuddhveermahindrakar]

विविध भौमितिक आकृत्या, त्यांचे अनंत विभाग करून त्यांची बेरीज , प्रात्यक्षिकासह दर्शवल्यामुळे अनेक घटकांची माहिती मिळाली, यामुळे विविध कल्पना सुचतात, भूमिती मध्ये लपलेल्या सौंदर्याच दर्शन घडले
धन्यवाद सर

[kornelviktor]

By far the most beautiful and relaxing video on youtube thanks :)

[Shdowbanned]

I've seen this explained in an analogy of folding infinity, somehow making it a finite number. As in, fold S, get S+1. Like a weird rule

[corentinz]

is this a patern ? like sum (1 -> infinity) 1/k^i = 1/(k-1) ?

[Smashachu]

The reason why i've always struggled with math is because i'm a very visual person.I feel like the difference between just knowing how to do math and knowing how math works and why things are the way they are adds a whole depth to the subject that is never taught in schools. A depth that allows you to understand the world around you better. Once you can look at a circle and fully understand what pi is, then you will never look at a circle the same way again. You will constantly have that teaching reinforced because it enhanced your understanding of the world. Which is why we invented math in the first place.

[theoriginaldrpizza]

Awesome job putting this together! I had never seen many of those before.

[sciencetechnician]

Amazing geometrical proof on GP, I am really happy that I had learnt something new..

[ChannelDefault]

Your channel is underrated. This is really beautiful and artistic.

[vyacc.friend]

OMG, it is so beautiful! I have learned something about applied math in art and also some number mathematics! Thank you!

[Mathius]

I love the concept of algorithmic art and math as art. This is wonderful.

[lapis.lareza]

Thank you, thank you very much for the beautiful works !

[DoxxTheMathGeek]

With math you can create really nice looking things like fractals, geometric series, etc.
I still can't understand how most people don't like math.

[-ZH]

5:00
Just realised this proof can be used for any of the sums, as long as you find a way to evenly divide the area of the triangle.

[TRZG]

Please don't stop making these videos they are helpful

[KaliFissure]

I had no idea you had then all in one place.
How beautiful and perfect that the infinite sum is the previous fraction. It can't help but be such and yet

[Zangoose_]

Math Degree here. This makes me feel like "All that challenging work don't seem so hard no more."