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Discovery of Classic Pi Formula a ‘Cunning Piece of Magic’

posted by martyb on Friday November 13 2015, @10:14PM   
from the it's-only-half-a-Tau dept.

Phoenix666 writes:

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."

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Original Submission

• Re:Inverse-square laws and spherical symmetry (Score: 0) by Anonymous Coward on Saturday November 14 2015, @02:50AM

  by Anonymous Coward on Saturday November 14 2015, @02:50AM (#262998)

  it shouldn't be so surprising to find π popping everywhere when you are dealing with fields with those properties, although that a specific representation of π should arise so naturally is indeed interesting.

  Interesting yes, shocking- not so much (perhaps, to the limited extent of my ability to add value to this conversation). A good parallel situation perhaps is a recent article I read on some insect, maybe it was a grasshopper like thing, that had evolved literal gears. Here seeing the human 'invention' of gears evolve naturally in the biosphere is interesting, but again, not so shocking. Though focusing on the specific representation, I would guess that the representation is part of the specific quantum mechanics situation going on here (similar to your mention of spherical em fields). I just imagine e.g. trying to use genetic algorithms to emerge small algorithms to represent pi, and presumably you'd see a large fraction hit the same sorts of simplest solutions humans have worked out thus far. In a similar fashion, i'm not surprised to see natural systems like the one this quantum model is representing, stumble/settle upon some simple solution.

  Parent