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Date : 1732457892595 - unknown on Apple WebKit
Mystery text : QlVCQUhtRVJrT3cgaSAgbG92ICB1IGV1LXByb3h5LnBva2V0dWJlLmZ1bg==
143 : true
242,842 Views • Apr 29, 2024 • Click to toggle off description
If you like this content, you can support my work at www.buymeacoffee.com/VisualProofs Thanks!
Also, check out my playlist on geometric sums/series: • Geometric Sums
This animation is based on a proof by The Viewpoints 2000 group from the October 2001 issue of Mathematics Magazine page 320 (www.jstor.org/stable/2691106 ).
#mathshorts #mathvideo #math #calculus #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricsums #series #infinitesums #infiniteseries #geometric #geometricseries
To learn more about animating with manim, check out:
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Views : 242,842
Genre: Education
License: Standard YouTube License
Uploaded At Apr 29, 2024 ^^
warning: returnyoutubedislikes may not be accurate, this is just an estiment ehe :3
Rating : 4.894 (416/15,333 LTDR)
97.36% of the users lieked the video!!
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User score: 96.04- Overwhelmingly Positive
RYD date created : 2024-10-07T17:41:18.451642Z
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150 Comments
Top Comments of this video!! :3
Very neat perspective on the converging geometric series
67 |
As the video proceeded, I saw myself learning something new and actually useful.
Thank you!
168 |
Neat proof, I'm trying to recall long ago how we handled converging series... and once again those isosceles triangles are so underrated
3 |
very very elegant
24 |
Thats brilliant. Keep making cool videos like these mate
22 |
There is a small detail, the lines only intersect if r<1, so the sum is not valid if r>=1
21 |
Excellent proof - thank you!!!!
2 |
This is a brilliant visual proof! Thank you!
2 |
The beauty of the geometric series that you can demonstrated its sum with cool way like this besides the analytic way, and your explanation is good, great video
|
What a beautiful proof. Thank you for making this.
5 |
Wow, it looks cool
2 |
doing this right now in calc 2. this is actually really helpful
1 |
Great way of proving.
1 |
i love this proof, it’s so easy to derive i literally never will learn the formula except temporarily
1 |
really cool proof, and I love the way you explained it, minus it going by a bit fast and me needing to pause a couple times to take it in
41 |
Its interesting that this proof also shows why we need r<1 because if r>1, the lines would get further apart and never interesct.
However, I wonder if there is a variation of this proof that could get work for negative r values. That would be very interesting
39 |
Try doing the algebra starting with x= rx+a and solve for x. x-rx = a. x(1-r) = a. x = a/(1-r)
1 |
Genuinely beautiful
1 |
this is incredible
1 |
@МаксимАндреев-щ7б
6 months ago
This picture is like the picture for the trigonometric proof of Pythagorean theorem
490 |