New Pi Formula (the extra physics bit) - Numberphile
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- Опубликовано: 15 окт 2024
- The main video is at • New Recipe for Pi - Nu... and the interview with Sinha and Saha is at • Pi-oneers (interview w... --- More links & stuff in full description below ↓↓↓
The paper on Physics Review Letters: journals.aps.o...
And on arxiv: arxiv.org/abs/...
The Case for String Theory: • The Case for String Th...
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The main video is at ruclips.net/video/nXexsSWrc1Q/видео.html and the interview with Sinha and Saha is at ruclips.net/video/2lvTjEZ-bbw/видео.html
Thank to you, care.
I've heard "is is" entering most people's vocabulary enough in recent years, but at 4:28 Tony pulls out a rare "is is is." Quite impressive!
"is is" is part of a cleft sentence.
The thing about cats is...
The reason why is..
Where it is is...
The thing is that some people have started saying it outside of this, or in cleft sentences that don't need it. "the thing is is"
@@therabbithat yes, and that sentence construction has gotten more popular recently to the point where, in almost every video or conversation, someone will eventually use "is is" as if it's a single word.
Pi and pions are related after all!🤣🤣🤣 It is hilarious that someone asked "How are pions related to the number pi" and got a no.
No backwards is on. Pi-on
well, there are approximatley pi types of pions, or exactly floor(pi).
Great work! I love it when we get more details about these stories.
I love watching Tony get excited about new papers & results. His joy is infectious 😁😁😁
I love numberphile so much
He makes a strong case the paper is interesting in a way totally unrelated to the pi thing haha
When you've just come up with a new way of doing a calculation, it's useful to put in some values where you know that the right answer is something well-known but not trivial. You can be pretty sure you haven't made a mistake if you find a new series that your result says will converge to pi, and taking a lot of terms gives a result that's very close to pi. If you come up with a way to calculate expressions that nobody know the answer to, it's hard to tell whether you have a typo along the way.
So they found a way to make the string theory equivalent of an effective field theory? Did I get that right?
Exciting things coming g from string theory.... in 10 years... lol🎉😂
Extraordinary visual output in this video re: CERN.
Could this imply that now some part of string theory can be tested?
Considering how complicated the formula is, does it give better approximation when computation cost is considered rather than just the number of steps?
On another note, does it make string theory actually falsifiable?
Recipe for Pi, haha, I got that one.
6:23 On-Screen (towards the bottom): *".....new....representations of....π, which show fast convergence."*
In the 'Part 1' video, it was discussed how the convergence of this new formula was extremely slow, and the authors stated that they never claimed that it was fast.
And yet I see, "...π....fast convergence."
Is the π symbol quoted above the common 3.14..., or is it something else? (Just in case that's the explanation.)
🙂🙂🙂🙂🙂🙂🙂 .: confused :. 🙂🙂🙂🙂🙂🙂🙂
I don’t think anyone said it was “slow”… the authors just said they were not claiming it was revolutionary.
How fast or slowly it converges of course depends on lambda. High values of lambda of course do make it slow (Madhava speeds)
But no matter what you set as lambda, it is not in the Chudnovsky ballpark.
The media sensationalized the claim and said it was extremely fast by modern standards. It wasn't but it doesn't mean the convergence is slow, it's still amazingly fast, just not like SOTA.
Am I right that the Beta(1/2,1/2) gives not pi exactly, but (sqrt(pi)/2?
That's pretty neat.
Did we learn something important about Euler function or not?
Fun stuff
One question, why use this pi formula when we faster ones?
I think everyone in the video made it clear that this was just an interesting byproduct of their research and it was not published to offer a more efficient or accurate way of calculating pi. The importance of publishing these side notes is that someone in future might pick the baton up and develop it into something more useful. Most of the gamechanging scientific and engineering developments we now take for granted came about this way.
@@nrml76 got it, cool
Could someone tell me a source for the graph found at 2:40?
Tanc 2D plot
@@tinto278 somewhat similar but not the same
Tony uses a Mac and not a NeXT..😬
I found a new way too!
[(cos²π + sin²π)-1+π] 😅
So nice!
Why is this unlisted??? I can't find it by searching
It will be publicly listed later.
Normally, it is strictly ruled.
Beta function regularization!
Enjoyed this more than a skeptical observer should?
Euler's e-Pi-i 1-0-infinity superposition identification only needs a Geometer to rewrite the process of Scattering in Unit Circle modulo-geometrical Superspin-spiral Singularity-point interference, and everyone will be happier about why String Theoretical reasoning corresponds to log-antilog 2-ness i-reflection containment in 3-ness Cavity Resonance of Logarithmic Time Duration Timing Conception.
Hmmm B(1/2, 1/2) = PI? if B(x,y) is x!+y!/(x+y)! then (1/2!+1/2!)/(1!) is 1.77 which isn't pi. Don't understand that part.
The key thing here is that.
Gamma(1/2) = sqrt(pi) and
Gamma (1) = 1
So, B(1/2, 1/2) = [gamma(1/2) * gamma(1/2)] / gamma(1/2+1/2)
-> B(1/2, 1/2) = [sqrt(pi) * sqrt(pi)] / 1
-> B(1/2, 1/2) = pi
Hope this helps!
Gamma(n) = (n-1)!
Gamma(1/2) = (-1/2)! = sqrt(pi)
Gamma(1) = 0! = 1
B(x,y) = Gamma(x)*Gamma(y)/Gamma(x+y)
B(1/2,1/2) = Gamma(1/2)*Gamma(1/2)/Gamma(1) = sqrt(pi)*sqrt(pi)/1 = pi
The Gamma function isn't _identical_ with factorial (look it up on Wiki, it's a funny-looking integral); it just so happens to behave in the same way when its argument is a positive integer. This is related to what mathematicians call 'analytical continuation': the Gamma function 'continuates' (or extends) the factorial operation.
The Gammas on the top of the expression are multiplied, not summed.
You got the beta function wrong. B(x,y) = Γ(x)Γ(y)/Γ(x+y), and Γ(1/2)=√ π.
It's already discussed a year ago by Indian physicist 😂
When you have a useless physical theory in the short and medium term, but it goes one way and hits something else 👆🦍
I say this because over the decades and tons of information stored, it will become something splendid.
That is an obscene formula.
Actually this is not right, because it has no mathematical fundations, with respect to the academic issue.
*Garbage!* There's only ONE accurate formula for Pi , and that's... *Viète's formula.*
The reason is because it containts infinity, 1, 2, half of one... andf most importantly square root of 2.
It has to do with the circle and the infinity of right triangles inscribed in the circle, where the hypotenuse is the diameter of the circle... and from this infinity of inscribed right triangles, there is only ONE isosceles triangle (if you use only half of the circle), with sides 1 and hypothenuse being square root of 2.
I guess as pi being defined as half the circumference of a unit circle, you need to address that fact in the formula. Anything else is number theory voodoo.