Pi - Who Comes Up With the Numbers After 3.14?

Here’s Mathematician KP Hart’s Math Question and Answer for today! Read it, sear it onto your brainpan and take it to the water cooler to impress all your co-workers!

Who invents Π?

“Who invents the endless series of numbers after 3.14?”

Answer:

The short answer: nobody.

The long answer: nobody, because that sequence of digits is already determined. The number π once was defined as the ratio of the length of a circle and the length is a diameter. When, in the 19th century, mathematicians put Mathematical Analysis on firm foundations it became clear that this definition was not the most workable one. In the end, the statement “π is the length of a circle with diameter 1” a theorem.

For practical purposes and in order to do something with formulas involving π it would be nice to have an exact numerical expression for it, say as a fraction, or something with some (square) roots in it, but it was proven in the 19th century that that is not possible. We can, therefore, at best make approximations and because the decimal representation has become the one of choice we look for decimal approximations in particular.

There are many formulas for π but there is, as yet, no formula that produces a desired decimal at once: if you want the thousandth decimal you will have to calculate the preceding 999 decimals as well.

A better question, therefore, is “Who comes up with a formula for the decimal expansion of π?”

More has been written about π than probably any other number in Mathematics. Its Wikipedia page is a good place to start exploring: π on Wikipedia.

About Dutch Mathematician KP Hart: In the beginning of this year the Dutch government opened a website, The Dutch Science Agenda, where everyone could post questions that they thought were of scientific interest. This was an attempt to involve the whole country in determining what the Dutch science agenda should be in the coming years.

I looked through the questions and searched for terms like `mathematics’, `infinity’ … to see what mathematical questions there were and I noticed various questions that already have answers (and have had for a long time). On a whim, I decided to post answers to those questions, in Dutch. For your edification, I will translate these posts into English.

This article was originally published 8/31/2015.