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"The various formulae look like they were inspired by the hallucinations of a mathematical poet. Among the simplest is a peculiar polynomial in π: 4π3 + π2 + π. Another takes the algebraic form (9/16π4)(π5/5!)1/4, and a third involves the 10th and 33rd prime numbers, 29 and 137, and takes the shape (29/π)cos(π/137)tan(π/29·137). A further formula in the collection is the strikingly simple (π2 + 1372)1/2.

What draws these formulae together is that they are all remarkably close approximations to a number that physicists know very well: the so-called fine structure constant, α = e2/?c, which plays a fundamental role in the quantum theory of electrodynamics. Arnold Sommerfeld first introduced α into physics in 1916 when proposing relativistic corrections to Bohr's model of the atom — corrections that gave 'fine structure' to its energy levels and to atomic spectra, hence the name. Later, during the development of quantum field theory, α emerged as a far more profound dimensionless number linking quantum theory with electrodynamics and relativity."
Nature Physics