Why is Pi so Special?
Good question. Pi is an “irrational number” which has an unending decimal expansion. π is an irrational number, meaning it cannot be referenced exactly as a fraction, but only as a decimal which never ends or repeats. The current world record has π at a value with some ten trillion decimal points of accuracy. In a practical sense, a physicist needs only 39 digits of π to make a circle the size of the universe accurate to the size of a hydrogen atom. Another way to think about pi is that it doesn’t occupy one specific place on the number line. Yes, it is 3.14… so it falls somewhere between 3 and 4, or between 3.1 and 3.2 as in the diagram below. The level of accuracy depends how much you magnify the number line – or how close you get to the position of pi. Pi acts more like a vibrating violin string – never still in one place, but close to a fixed place. This is quite weird but, in many ways, Pi reflects the uncertainty of our universe itself and perhaps the very nature of life?
Here is another way to define the position of pi (click in space or refresh your browser if nothing appears):
Source is here