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What's the significance of pi?by Naty1
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#1
Jan913, 05:37 PM

P: 5,632

Back in 2008 I posted the same topic [thread now closed, due to age??:
C:\Users\Owner\Documents\PHYSICS\What's the significance of pi.mht We missed a fascinating answer I just noticed: In natural units, commonly used in high energy physics, where the Coulomb constant is 1/4π and c = ħ = 1, the value of the fine structure constant is α = ε^{2}/∏ http://en.wikipedia.org/wiki/Coupling_constant and is also a component of the gauge coupling constant..... 


#2
Jan1013, 02:35 AM

P: 534

Pi is just the universal constant of rotation, of curvature. What does 3.14…. mean? I don’t know, why don’t we just set it to one and meditate on how profound it is. What I want to know is how many decimal places do we need to go before a circle is a perfect circle as far as we can tell 1) psychophysically, and 2) practically as far as engineering applications. I think that would be an interesting figure.
One more thing, Pi may actually be overrated. Have you heard of Tau? Tau is just 2 time Pi, and it seems even a more parsimonious and natural number to use than Pi. See Khan’s cool talk on it. http://www.youtube.com/watch?v=1jDDfkKKgmc However, I don't think we're gonna see a conversion here soon among contemporary scientists and engineers any more than we saw a swift conversion to the metric system in the USA. 


#3
Jan1013, 02:38 AM

P: 534

BTW, is that squiggly E you used in the fine structure constant equation the permitivitty of free space or something else?



#4
Jan1013, 02:39 AM

Admin
P: 23,369

What's the significance of pi?
http://www.physicsforums.com/showthread.php?t=263423
Some time ago micromass showed me a nice infinite sum expressing pi using prime numbers, but I can't remember it right now and quick googling didn't yield it. 


#5
Jan1013, 06:43 AM

P: 5,632

who knows....it's from the 'quick symbol' list on the right of my screen when I post... It doesn't look quite right, but I figured 'close enough' !! 


#6
Jan1013, 06:46 AM

Mentor
P: 16,966

[itex]\pi[/itex] is highly significant, with p<.0001



#7
Jan1013, 11:52 AM

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P: 18,036

http://en.wikipedia.org/wiki/Riemann_zeta_function 


#8
Jan1013, 01:56 PM

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#9
Jan1013, 10:37 PM

P: 17

I think this is from Dirac  (4pi^3 + pi^2 + pi^1)^(1) = finestructure constant (to a surprisingly good accuracy!)



#10
Jan1013, 11:27 PM

P: 534




#11
Jan1013, 11:37 PM

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#12
Jan1113, 12:15 AM

P: 2,784

Hey Borek,
Mathworld had the series equivalent to get pi/4 called the Gregory Liebnitz series: pi/4 = 1  1/3 + 1/5  1/7 ... http://mathworld.wolfram.com/PiFormulas.html 


#13
Jan1113, 12:31 AM

P: 17




#14
Jan1113, 12:36 AM

P: 2,251

in any units: [tex] \alpha \ = \ \frac{e^2}{(4\pi\epsilon_0) \hbar c} [/tex] depending on the variant of "natural units" 3 of the four variable symbols on the right can go to 1 (or any other predetermined constant). 


#15
Jan1113, 02:33 AM

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P: 23,369

Or at least that's how I see it, I can be wrong (and happy with it ). 


#16
Jan1113, 08:36 AM

P: 2,784

In contrast, there was the story of how pi was embedded within the measurements of the pyramid as in 100 cubits high vs 100 pi cubits on edge. Whereupon an engineer figured that the designers had rolled a 1 cubit diameter disk a hundred times to measure out the edge. (not sure if its true or a 4500 yr old urban legend) 


#17
Jan1113, 11:48 AM

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P: 11,589

137.036303775878 = 4pi^3 + pi^2 + pi^1 137.035999074(44) = 1/alpha Deviates by 0.0003, this corresponds to ~7000 standard deviations of the uncertainty. 


#18
Jan1413, 04:18 PM

P: 534




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