The number 137
In the Bohr atomic model, the innermost electron of a hypothetical atom with atomic number 137 would be orbiting just below the speed of light, and the next heaviest element would be impossible because its electron would have to exceed c. Atoms close to the theoretical limit of 137 are unstable and not found in the universe.
The fact is, the fine structure constant is not exactly 1/137. The currently accepted value is 1/137.035999074 (CODATA 2010). The denominator of the constant is called α (alpha) and it is slightly larger than 137.
In order of increasing accuracy, here are various thinkers’ attempts to discover the math behind 1/α.
Feynman called Euler’s Identity “our jewel” and “the most remarkable formula in mathematics.” It normally takes the form you can read about on Wikipedia but I came across an alternate formulation of Euler’s Identity in Xiao’s paper that I think is even more beautiful because it relates e, i (√-1), π, Ф, and ϕ, fundamental constants others have used to express α:
Read more : Why 137
The Golden Ratio
The illustration of the golden angle below is coincidentally exactly equal to Bohr’s formulation of alpha, 360/(Ф^2). The golden angle controls plant patterning of repeated biological units (called phyllotaxis) and governs the geometrical optics of rainbows.
Read more : The mysterious 137 (bible gematria)