Pi

The ratio of a circle's circumference to its diameter, the same fixed value for every circle regardless of size, and one of the two or three most famous constants in mathematics. Babylonian and Egyptian sources approximate it numerically as early as the second millennium BCE; Archimedes gave the first rigorous method for bounding it, using inscribed and circumscribed polygons of increasing sides to trap its value between two close bounds, around 250 BCE. It is irrational (Johann Lambert proved this in 1761) and transcendental (Ferdinand von Lindemann proved this in 1882, which also settled, negatively, the ancient problem of squaring the circle by compass and straightedge). The Greek letter symbol itself was popularized, though not invented, by Leonhard Euler's adoption of it in the 1730s and 1740s.