Mathematics
What is Pi? The Most Famous Number in Mathematics
Explore the fascinating history and properties of Pi (π), the irrational number that defines all circles.
What is Pi (π)?
Pi (π) is perhaps the most famous number in mathematics. It represents the ratio of a circle’s circumference to its diameter and is approximately equal to 3.14159265358979.
Key Properties of Pi
- Irrational: Pi cannot be expressed as a simple fraction. Its decimal representation never ends and never settles into a permanently repeating pattern.
- Transcendental: Pi is not the root of any polynomial equation with rational coefficients.
- Universal: Every circle in the universe has the same circumference-to-diameter ratio: π.
A Brief History
Ancient Civilizations
- Babylonians (~1900 BC): Approximated π as 3.125
- Egyptians (~1650 BC): Used 3.1605 in the Rhind Papyrus
- Archimedes (~250 BC): Calculated π between 3.1408 and 3.1429
Modern Era
- Ludolph van Ceulen (1596): Calculated 35 digits
- Computer age: Billions of digits now known
- Current record: Trillions of decimal places
Pi in Formulas
| Formula | Description |
|---|---|
| C = πD | Circumference from diameter |
| C = 2πR | Circumference from radius |
| A = πR² | Area of a circle |
| V = (4/3)πR³ | Volume of a sphere |
Pi Day
Pi Day is celebrated on March 14 (3/14) each year, corresponding to the first three digits of π. In 2015, Pi Day was extra special at 3/14/15 9:26:53, representing π to 10 digits.
Fun Facts
- Pi has been calculated to over 100 trillion decimal places
- There is no pattern in pi’s digits — they appear random
- The symbol π was first used by Welsh mathematician William Jones in 1706
- Albert Einstein was born on Pi Day (March 14, 1879)
Try our circumference to diameter calculator to see π in action!