π is one of the fundamental constants of mathematics: the ratio of a circle's circumference to its diameter.
π is an irrational number — it can never be written as a fraction of two whole numbers, and it does not have a terminating or repeating decimal expansion. The decimal expansion of π goes on forever, never showing any repeating pattern. Since π is irrational, all we can ever hope to do is get better and better decimal approximations.
So, how did the ancients first approximate π?