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Pi number, being the most famous mathematical constant, as it turned out to fit perfectly into our real world, because for sure reflects the location of the possible “orbits” of electrons in atoms.
This is the conclusion reached by the American physicist Carl Hagen (Karl Hagen) and mathematician Tamar Friedmann (Tamar Friedmann), working at the University of Rochester.
It all started with what Hagen offered his students use Schrödinger formulas to calculate energy levels in the hydrogen atom and then compare them with the already known, obtained by physicists during numerous experiments and calculations.
Naturally, the teacher himself solved this problem in parallel, in order to demonstrate to students how to do this. During such Karl noticed to his surprise in the structure of the orbits electrons some mathematical regularity, or rather – geometric progression. Being interested in this, the physicist turned for help to the mathematician Tamar Friedmann.
Friedmann, in turn, remembered that back in 1655, the British John Wallis derived the mathematical formula of the infinite a series of multiplied fractions, with the help of which it was calculated Pi constant – 2/1 * 2/3 * 4/3 * 4/5 * 6/5, well, etc. It turned out that the Wallis formula corresponds with surprising accuracy to geometric progression between the properties of energy levels hydrogen atom.
This discovery, says Friedmann, literally shocked us with Karl. It turns out that between abstract mathematical and real the physical world has a strong bond. Moreover, we have discovered and one more regularity – the farther the particle from the nucleus of the atom, the more of her orbit tends to an ideal circle. That’s how we managed combine math with physics three hundred and sixty years after Wallis’ discovery of the purely mathematical constant Pi.
You can familiarize yourself with the findings of American scientists in more detail. in the scientific journal Journal of Mathematical Physics, where she was a large article has been published on this subject.
