**A Classic Formula For Pi Has Been Discovered Hidden in Hydrogen Atoms**

https://reasonandscience.catsboard.com/t2554-a-classic-formula-for-pi-has-been-discovered-hidden-in-hydrogen-atoms

Suppose we found an actual formula for calculating Pi embedded in nature somewhere. Not the value of Pi, but the formula for calculating Pi. Is that the sort of evidence that would be sufficient to provide evidence of God's existence?

A Classic Formula For Pi Has Been Discovered Hidden in Hydrogen Atoms

https://www.sciencealert.com/a-classic-formula-for-pi-has-b…

Since 1655 there have been plenty of proofs of Wallis's formula, but all have come from the world of mathematics, and the new results have people freaking out. The results have been published in the Journal of Mathematical Physics.

"This almost seems like magic," writes maths contributor Kevin Knudson for Forbes. "That a formula for π is hidden inside the quantum mechanics of the hydrogen atom is surprising and delightful."

"Nature had kept this secret for the last 80 years," said Friedmann. "I'm glad we revealed it."

We just can't help but wonder what other secret connections are lurking between quantum mechanics and pure mathematics.

a secular physicist said: well that's some piece of magic you got there.

It's a miracle on its face that the formula for calculating Pi is embedded in the hydrogen atom, not the value of Pi, but the actual formula.

Formulas for calculating things are mental constructs and yet here is this mental construct embedded in the atom we most associate with circles.

Following the link to the scientific paper:

http://aip.scitation.org.sci-hub.cc/d…/abs/10.1063/1.4930800

the authors write:

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. was derived by Wallis in 1655

by a method of successive interpolations. While several mathematical proofs of this formula have been put forth in the past (many just in the last decade) using probability, combinatorics and probability, geometric means, trigonometry, and trigonometric integrals, there has not been in the literature a derivation of Eq. (1) that originates in physics, specifically in quantum mechanics.

It is the purpose of this paper to show that this formula can, in fact, be derived from a variational computation of the spectrum of the hydrogen atom. The existence of such a derivation indicates that there are striking connections between well-established physics and pure mathematics that are remarkably beautiful yet still to be discovered.