What is Pi?


What is Pi exactly? Who came up with the deliciously mysterious math phenomena? Why is it important?

Pi is the 16th letter (π) of the Greek alphabet which is used to represent this mathematical constant.It is typically written as "pi" in text.

Pi is, by definition, the ratio of the circumference of a circle to its diameter. Regardless of the circle you use to calculate pi, it is always the same number.

Pi is an irrational number, meaning it is a real number with a nonrepeating decimal expansion. That is to say, it cannot be represented by an integer ratio. This means that pi goes on FOREVER, also known as an infinite decimal.

Pi is a transcendental number, meaning it is a number which is not algebraic. That is to say, it is not a root of a non-constant polynomial equation with rational coefficients.

Approximating Pi

For many purposes, people need to approximate the value of pi. Obviously, the more decimal places you use, the more accurate a measurement you will get.

Many students are introduced to pi by with the value of 3.14. As they proceed in their studies, they then typically represent pi as 3.14159, then on to 3.14159265. From there, it just gets longer.


There are several rational expressions to estimate pi. Here are a few, listed in order of increasing accuracy:

  • 3

  • 227

  • 333106

  • 355113

  • 103993/33102


Here is an image that also helps visualize the estimate of pi:



A Brief History of Pi

I can't pretend to give a full out history of pi. It is a very old number, dating at least to time of Ancient Egypt. Several ancient mathematicians have pondered pi, including Archimedes and Ptolomy. As civilization has modernized, more and more accurate estimates of pi have been discovered, including pi to the milliions of digits.