The mathematical constant approximately equal to 3.14159, the ratio of a circle's circumference to its diameter.Pi (π) is the ratio of a circle's circumference to its diameter, a constant that appears throughout mathematics and physics. Its value is approximately 3.14159, but it is an irrational number, meaning its decimal representation never ends and never repeats. Pi emerges naturally in any context involving circles, spheres, or periodic phenomena, from the geometry of a wheel to the quantum mechanical description of an electron's wavefunction.
The concept of pi has been known for thousands of years, with ancient Babylonians and Egyptians approximating it. The Greek mathematician Archimedes (c. 287–212 BCE) rigorously bounded its value between 3.1408 and 3.1429 using inscribed and circumscribed polygons. The symbol π was first used by Welsh mathematician William Jones in 1706 and popularized by Leonhard Euler in the 18th century.
Pi arises from the fundamental relationship between a circle's circumference (C) and its diameter (d): C = πd. This definition extends to areas (A = πr²) and volumes of spheres (V = 4/3πr³). In physics, pi appears in formulas for oscillations, waves, and rotations because these involve circular motion or periodic cycles. For example, the period of a simple pendulum or the wavelength of a standing wave both involve pi.
Pi is used in engineering for designing circular structures, in GPS and navigation for spherical geometry, and in signal processing for Fourier transforms that decompose waveforms into circular components.
The record for the most digits of pi computed is over 100 trillion, but only about 40 digits are needed to calculate the circumference of the observable universe to within the width of a hydrogen atom.
| t_{\text{rip}} - t_0 | variable | Time remaining until Big Rip — time interval second |
| w | variable | Equation of state parameter — equation of state parameter |
| \rho_0 | variable | Current dark energy density — energy density joule per cubic metre |
| G | constant | Constant of gravitation in Newton's law — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| \pi | constant | Ratio of circle circumference to diameter — pi = 3.14159 |
| β | variable | Plasma beta — plasma beta |
| p | variable | Plasma pressure — pressure pascal |
| B | variable | Magnetic field strength — magnetic field tesla |
| π | constant | Mathematical constant — pi = 3.14159 |
| L | variable | Intrinsic luminosity — luminosity watt |
| D_L | variable | Luminosity distance — photometric distance metre |
| F | variable | Observed flux — flux watt per metre squared |
| k(λ) | variable | Extinction curve at wavelength λ — extinction curve |
| E(B-V) | variable | Color excess between B and V bands — color excess |
| π | constant | Ratio of a circle's circumference to its diameter — pi = 3.14159 |
| B(E1) | variable | Electric dipole reduced transition probability — reduced transition probability coulomb squared metre squared |
| Z | variable | Atomic number (number of protons) — atomic number |
| e | variable | Elementary charge — elementary charge coulomb |
| ⟨r²⟩ | variable | Mean square radius of the charge distribution — mean square radius metre squared |
| π | constant | Ratio of a circle's circumference to its diameter — pi = 3.14159 |
| L_Edd | variable | Eddington luminosity — luminosity watt |
| M | variable | Mass of the object — mass kilogram |
| κ | variable | Opacity of the stellar material — opacity square metre per kilogram |
| G | constant | Constant of universal gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| π | constant | Mathematical constant pi — pi = 3.14159 |
