The Number π
Pi is the ratio of any circle's circumference to its diameter. It's the same for every circle in the universe — and it's been fascinating mathematicians for more than 4,000 years.
The short definition
Pi, written with the Greek letter π, is a mathematical constant approximately equal to 3.14159265358979…. Its definition is astonishingly simple: take any circle in the world, divide the distance around it (the circumference) by the distance across it (the diameter), and you always get π.
Because pi is an irrational number, that decimal never ends and never falls into a repeating pattern. Because pi is also transcendental, it's not the solution to any polynomial equation with rational coefficients — which is why you can't "square the circle" with compass and straightedge.
A brief history of the pi number
- ~2000 BCE — Babylonians and Egyptians approximate pi as 3.125 and 3.16 respectively.
- ~250 BCE — Archimedes uses inscribed and circumscribed polygons to bound pi between 3.1408 and 3.1429.
- 400s CE — Chinese mathematician Zu Chongzhi computes pi to 7 digits, a record that held for 900 years.
- 1706 — William Jones is the first to use the letter π for this ratio. Euler popularizes the notation.
- 1761 — Johann Lambert proves pi is irrational.
- 1882 — Ferdinand von Lindemann proves pi is transcendental, settling "squaring the circle" once and for all.
- 1949 — The ENIAC computer computes pi to 2,037 digits in 70 hours.
- Today — Pi has been computed to over 200 trillion digits on purpose-built hardware.
Why π matters
Pi is the glue that holds geometry and trigonometry together. But it also shows up in places that have nothing obvious to do with circles: statistics (the normal distribution), number theory (the Basel problem, ζ(2) = π²/6), physics (Heisenberg's uncertainty principle), and even probability (Buffon's needle). Wherever there's symmetry, rotation, or oscillation, pi sneaks in.