A Classic Formula For Pi Is Hidden in Hydrogen Atoms

Back in 2015, scientists found something amazing – a classic formula for pi hidden in the world of quantum physics.

Pi is the ratio between a circle’s circumference and its diameter, and is incredibly important in pure mathematics. But this was the first time scientists had found it “lurking” in the world of physics, when using quantum mechanics to compare the energy levels of a hydrogen atom.
Why was that exciting? Well, it revealed an incredibly special and previously unknown connection between quantum physics and maths.

“I find it fascinating that a purely mathematical formula from the 17th century characterises a physical system that was discovered 300 years later,” said one of the lead researchers at the time, Tamar Friedmann, a mathematician at the University of Rochester in the US.

The discovery was made when Carl Hagen, a particle physicist at the University of Rochester, was teaching a class on quantum mechanics and explaining to his students how to use a quantum mechanical technique known as the ‘variation principle’ to approximate the energy states of a hydrogen atom.

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