A famous pre-Newtonian formula for π is obtained directly from the variational approach to the spectrum of the hydrogen atom in spaces of arbitrary dimensions greater than one, including the physical three dimensions.

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For an example of such a connection, see,
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For example, the ratio is 0.849, 0.906, 0.932, 0.978, 0.998 for ℓ = 0, 1, 2, 10, 100.

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