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143 : true
19,367 Views • Aug 8, 2024 • Click to toggle off description
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For a longer, wordless version (more dramatic) of this animation see
• Geometric series: sum of powers of 1/...
Also, check out my playlist on geometric sums/series: • Geometric Sums
This animation is inspired by the a proof by Elizabeth M. Markham from the October 1993 issue of Mathematics Magazine page 242 (doi.org/10.2307/2690738).
#mathshorts #mathvideo #math #calculus #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #geometricsums #series #infinitesums #infiniteseries #geometric #geometricseries #square
To learn more about animating with manim, check out:
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Views : 19,367
Genre: Education
License: Standard YouTube License
Uploaded At Aug 8, 2024 ^^
warning: returnyoutubedislikes may not be accurate, this is just an estiment ehe :3
Rating : 4.997 (1/1,293 LTDR)
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User score: 99.88- Masterpiece Video
RYD date created : 2024-08-28T23:23:30.482174Z
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65 Comments
Top Comments of this video!! :3
This is basically geometric progression in which the common multiple r has value less than 1 so show the formula to get sum of infinity a/(1-r) can be used ,its the same thing. Btw a is the first term in the above formula
2 |
1. Let 0.(n)=x
2. Multiply both sides by 10
n.(n)=10x
3. Substract x from both sides
n.(n)-0.(n)=10x-x
n=9x
x=n/9
4. Recall 0.(n)=x
0.(n)=n/9
1 |
So basically for any n, 0.nnn repeating will be equal to 1 in base n+1
22 |
I mean yeah you can do this with any fraction
37 |
Beautiful ❤️
3 |
The areas may be equal in measure, but there is a point in the center of the square that is never shaded. One way you can think of this is that the limiting difference between 0.888..._9 and 1.0 is an infinitesimal.
|
Isn't x-1 over x + x-1 over x² + x-1 over x³ ... always 1?
14 |
0.nnnnnn is 1 in base n+1
10 |
I've just realised that this videos of proving that something is 1 in base X is not as impressive since it's just like 0.999... is 1 in base 10 lol
1 |
0.99...=1 in base 10
3 |
How many series are left with these proofs?
2 |
Or we can be perfectly happy knowing that the area of the square is one square and go about the rest of our days without obsessing over tic tac toe boards. 😅
|
Good example how 0.99999... is equal to 1 (in base 10).
|
8/9=0,(8)≠1
1 |
You could also do 0.eee = 1 in hexadecimal.
8 |
Asymptoticism should be a word because this would be Antiasymtoticism
|
0.0000000... = 1 in base 1
3 |
Wouldn't it be more accurate to say it approaches 1 instead of equals 1?
1 |
(0.88888...)9=1
1 |
@UserYouTube506
3 months ago
Math in school: 🥱
Math in internet:
76 |