Pi

Symbol for pi

Pi is a mathematical constant and real number equal to the ratio between a circle's circumference and its diameter in the Euclidean norm. It occurs in many contexts, and the precise definition depends on the situation; often, it is convenient to define it as the absolute value of half the period of the complex exponential.

Formulae

Pi can be written with multiple formulae, many of which can be truncated to allow pi to be approximated to arbitrary precision. One of the best known formulae is the Chudnovsky formula, written as

$\displaystyle \frac{1}{\pi} = \frac{12}{640320^{3/2}} \sum_{k=0}^\infty \frac{(6k)! (13591409 + 545140134k)}{(3k)!(k!)^3 (-640320)^{3k}}$ , which can give fourteen correct digits of pi per term.

Information

Pi has been in use for thousands of years. Ancient Chinese, Egyptians and Babylonians had uses for Pi.

Trivia

• This page was created on March 14 2018, Pi day.