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17,046 Views • Oct 1, 2024 • Click to toggle off description
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This animation is based on a visual proof by Richard A. Gibbs from the June 1990 issue of Mathematics Magazine (doi.org/10.2307/2691137 - page 172).
#mathshorts #mathvideo #math #numbertheory #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #fractions #mediant #inequality #mathematics #fareyfractions #farey
To learn more about animating with manim, check out:
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Views : 17,046
Genre: Education
License: Standard YouTube License
Uploaded At Oct 1, 2024 ^^
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RYD date created : 2024-10-27T08:38:32.38576Z
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37 Comments
Top Comments of this video!! :3
A very nice visualization of the idea
17 |
Science is all about visualization ur doing the right job bro 🤜
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Thanks
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From the triangle shown, (a+c)/(b+d) >= c/d. Maybe the triangle is not drawn correctly. However, the issue with this visualization is, how did we assume that the slope a/b <= (a+c)/(b+d) ?
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Also known as naive fraction addition (since is the “wrong” way to add fractions when you first learn it 😂)
That aside, the mediant operation and the inequality are useful for finding rational approximations of irrational numbers using a method known as the Farey algorithm.
One small caveat is that you can only use the operation when the two fractions are in their simplest form i.e. irreducible in order to obtain a unique output from the operatio
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Or, define a Mediant function M(a, b, c, d)
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I think it works only if all the numbers are positive. (Of course a and c may be zero)
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Great content bro you are amazing ❤🎉
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What is that symbol at the end that has a plus + sign in a circle ⭕ ?
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I don't think this operation is well-defined. 3/6=1/2 but 3/6+1/5 isn't equal to 1/2+1/5.
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but it doesn't make sense still... because 1/2 ++ 2/2 is 3/4 but it's also equal to 2/4 ++ 1/1 which is 3/5 so... basically the result is anything inbetween the two parameters.
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Ok
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Please explain componendo Dividendo
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=≈
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the mediant is not well defined with respect to the representation chosen
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1st
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@claudiovijaya
1 month ago
Unbelievable.....power of computer animation...I never understood maths since 1986 math classes but now I see how simple was.. thanks for your content.
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