Every schoolchild will remember Π, pi, 22/7, that curious number you get when you divide the circumference of a circle by its diameter and which works out to a series of digits which no one has ever finished. Okay, it’s good for geometry and engineering, the Ancient Greeks knew that, but- so what else? Well the odd thing is that it seems to crop up in other branches of mathematics which are completely unrelated to geometry.
In today’s El Pais, Fernando Chamizo explains how. Take a very large number-call it N. Now multiply the products of all the even numbers that lead up to N. Call it q. Now the odd numbers and call it p. Divide p/q, square it and multiply that by 2N. You will get an approximation to Π. We tried it for N=10 and got 3.302, but as Fernando explains, the bigger the value of N, the closer you get to the real value of Π. Somehow our old friend pi is nested in the deep structure of the numbers.
It’s the same for Euler’s number, e , 2.718…which crops up all over the place in mathematics, compound interest, and computing, to paint the matter with a broad brush. And other abstruse things like imaginary numbers which equals the square root of -1.
And so we ask-is this a coincidence, a random consequence of numbers and algebra? Or is it a tiny hint, a clue of a clue if you like, to some deeper structure of reality which we have barely glimpsed? The potential dividends of such research might be enormous for us all. Instead of which we must spend our time dealing with the actions of a sociopathic tyrant whose learning is confined to some half digested mystical versions of history, and mopping up the blood which flows from it. (English speakers, get those translators ready!)
#mathematics #geometry #irrational numbers #imaginary number