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Pi (Π, π) Definition

Pi (Π, π) is the sixteenth letter of the Greek alphabet, representing the sound [p]. In the system of Greek numerals it has a value of 80. It was derived from the Phoenician letter Pe. Letters that arose from pi include Cyrillic Pe, Coptic pi, and Gothic pairthra.

Usage in Mathematics & Science

The uppercase Pi (Π) is used for:

  • The product operator in mathematics, indicated with capital pi notation Π (in analogy to the use of the capital Sigma Σ as summation symbol).

  • The osmotic pressure in chemistry.

  • The viscous stress tensor in continuum mechanics and fluid dynamics.

  • Other:

    • In textual criticism, Codex Petropolitanus, a 9th-century uncial codex of the Gospels, now located in St. Petersburg, Russia.

    • In legal shorthand, it represents a plaintiff.

The lowercase Pi (π) is used for:

  • The mathematical real transcendental (and thus irrational) constant π = 3.14159..., the ratio of a circle's circumference to its diameter in Euclidean geometry. The letter π is the first letter of the Greek words περιφέρεια periphery and περίμετρος perimeter, i.e. the circumference.

  • The prime-counting function in mathematics.

  • Homotopy groups in algebraic topology.

  • Dimensionless parameters constructed using the Buckingham π theorem of dimensional analysis.

  • The hadron called the pion (pi meson).

  • Economic profit in microeconomics.

  • Inflation rate in macroeconomics.

  • A type of chemical bond in which the p orbitals overlap, called a pi bond.

  • The natural projection on the tangent bundle on a manifold.

  • The unary operation of projection in relational algebra.

  • Policy in reinforcement learning.

  • Polyamory.

Greek Alphabet

The letters of the Ancient Greek Alphabet, which are frequently utilized in math and science:

Greek Alphabet

Symbol

Letter

Symbol

Letter

Uppercase

Lowercase

Uppercase

Lowercase

Α

α

Alpha

Ν

ν

Nu

Β

β

Beta

Ξ

ξ

Xi

Γ

γ

Gamma

Ο

ο

Omicron

Δ

δ

Delta

Π

π

Pi

Ε

ε

Epsilon

Ρ

ρ

Rho

Ζ

ζ

Zeta

Σ

σ

Sigma

Η

η

Eta

Τ

τ

Tau

Θ

θ

Theta

Υ

υ

Upsilon

Ι

ι

Iota

Φ

φ

Phi

Κ

κ

Kappa

Χ

χ

Chi

Λ

λ

Lambda

Ψ

ψ

Psi

Μ

μ

Mu

Ω

ω

Omega

Related Definitions

Sources

“Pi (Letter).” Wikipedia, Wikimedia Foundation, 17 Apr. 2020, en.wikipedia.org/wiki/Pi_(letter).

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