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While most people associate the mathematical constant π (pi) with arcs and circles, mathematicians are accustomed to seeing it in a variety of fields. But two University scientists were still surprised to find it lurking in a quantum mechanics formula for the energy states of the hydrogen atom.
"We didn't just find pi," said Tamar Friedmann, a visiting assistant professor of mathematics and a research associate of high energy physics, and co-author of a paper published this week in the Journal of Mathematical Physics. "We found the classic seventeeth century Wallis formula for pi, making us the first to derive it from physics, in general, and quantum mechanics, in particular."
The Wallis formula—developed by British mathematician John Wallis in his book Arithmetica Infinitorum—defines π as the product of an infinite string of ratios made up of integers. For Friedmann, discovering the Wallis formula for π in a quantum mechanics formula for the hydrogen atom's energy states underscores π's omnipresence in math and science.
"The value of pi has taken on a mythical status, in part, because it's impossible to write it down with 100 percent accuracy," said Friedmann, "It cannot even be accurately expressed as a ratio of integers, and is, instead, best represented as a formula."
(Score: 2) by maxwell demon on Friday November 13 2015, @10:28PM
That's true for any irrational number. Square root of two, cube root of five, golden mean, Euler constant, ...
The Tao of math: The numbers you can count are not the real numbers.
(Score: 4, Informative) by vux984 on Friday November 13 2015, @10:40PM
It cannot even be accurately expressed as a ratio of integers
That's true for any irrational number.
Actually that is the DEFINITION of a irrational number. That it can't be expressed as a ratio. That's literally what it means irrRATIOnal -> not-ratio-able aka "not expressible as a ratio"
However, I do think Pi is still more special than root2 or euler's constant just given how ubiquitous it and how many seemingly (emphasis on seemingly) unrelated ways there are to arrive at it.
(Score: -1, Offtopic) by Anonymous Coward on Friday November 13 2015, @10:41PM
> the DEFINITION of a irrational number
Actually they named it after my ex-wife.
(Score: 2) by jdavidb on Friday November 13 2015, @11:27PM
Actually that is the DEFINITION of a irrational number. That it can't be expressed as a ratio. That's literally what it means irrRATIOnal -> not-ratio-able aka "not expressible as a ratio"
Yes, but π has emotional issues and makes bad decisions.
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(Score: 1) by korger on Saturday November 14 2015, @07:47PM
However, I do think Pi is still more special than root2 or euler's constant just given how ubiquitous it and how many seemingly (emphasis on seemingly) unrelated ways there are to arrive at it.
Actually, pi and e are closely related, as expressed by the formula e^(pi*i)+1 = 0. There's an intrinsic beauty in this equation, which combines the five most important mathematical constants (0, 1, i, pi, e) into a single expression. As such, I'd reason that neither of these numbers is more special than the others, at least in the field of complex numbers.