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A 400 Years Old Classic Formula For Pi Has Been Discovered Hidden In Hydrogen Atoms

Scientists, for the first time ever, have discovered a classic formula for pi hiding in the world of quantum physics. Everybody is familiar with the word pi. It is the ratio among a circle's circumference and its diameter, and is extremely vital in pure mathematics, but now researchers have also found it "lurking" in the world of quantum physics, while using quantum mechanics to compare the energy levels of a hydrogen atom. 

So why is that even exciting? Well, it discloses an extremely special and previously unidentified connection between quantum physics and mathematics. It is quite interesting that a purely mathematical formula from the early 17th century portrays a physical system that was discovered 400 years later.
Image Credit: Benjamin Haas/

Carl Hagen, a particle physicist currently working at the University of Rochester, discovered this interesting connection while teaching a class on quantum mechanics and clarifying to his pupils how to use a quantum mechanical method identified as the 'variation principle' to estimate the energy states of a hydrogen atom. So while comparing these values to conventional calculations, Carl Hagen noticed an uncommon trend in the ratios. So he asked Friedmann to assist him work out this trend, and they rapidly realized that it was essentially an appearance of the Wallis formula for pi – the first time it had even been actually derived from physics.

Since 1655 there have been lots of verifications of Wallis's formula, but they all have come from the realm of mathematics, and the new outcomes have people stunned. The outcomes have been issued in the Journal of Mathematical Physics.
Two pages from Wallis's book Arithmetica Infinitorum Digitised by Google

Maths contributor Kevin Knudson for Forbes, wrote "This almost seems like magic. 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. I'm glad we revealed it." said Friedmann.

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

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