# University of Rochester Mathematicians Find Pi In Hydrogen Atoms

|### Pi – The Endless Number

Everyone knows about the unusual properties of the number pi – the ratio of the circumference of a circle to its diameter but even more fascinatingly, a number which never ends or repeats. Usually represented by the symbol π, pi turns up more often than you would think; the number appears in any number of mathematical formulas.

Interestingly enough, pi may be literally everywhere you look – mathematicians at the University of Rochester in Rochester, New York discovered pi in the structure of the way that the electrons in the hydrogen atom circle the proton. In case you were keeping score, hydrogen happens to be the most abundant element in the universe.

*See the article below for the surprise place scientists found the beloved Pi relationship …*

## Famed number π found hidden in the hydrogen atom

Adrian Cho – Nov 13, 2015

Three hundred and sixty years ago, British mathematician John Wallis ground out an unusual formula for π, the famed number that never ends. Now, oddly, a pair of physicists has found that the same formula emerges from a routine calculation in the physics of the hydrogen atom—the simplest atom there is. But before you go looking for a cosmic connection or buy any crystals, relax: There is probably no deep meaning to the slice of π from the quantum calculation.

Defined as the ratio of the circumference of a circle to its diameter, π is one of the weirder numbers going. Its decimal representation, 3.14159265358979 …, never ends and never repeats.

… Friedmann proved that for orbitals in which the electron whizzes around the nucleus with a lot of “angular momentum,” the ratio of the approximate and exact energies can be rewritten as the ratio of things called gamma functions. As angular momentum increases, the ratio of gamma functions narrows in on 1, explaining the efficacy of the approximation. Moreover, one of those gamma functions gives a value of π, whereas the other ones can be rewritten as the product of ratios in the Wallis formula. So with a bit of rearranging, the Wallis formula tumbles out. “I was completely surprised,” Friedmann says. “I wasn’t looking for it at all.”

The emergence of the formula probably doesn’t signal anything profound about quantum theory, cautions Bruno Nachtergaele, a mathematical physicist at the University of California, Davis, and editor of the journal in which the paper was published. “You are entitled to be delighted by this,” he says, “but one shouldn’t look too deep for meaning.” …

To read the full arcicle see ScienceMag.com

Cover Photo Credit: Geek3/Wikimedia/Creative Commons