Greek alphabet
Αα Alpha Νν Nu Ββ Beta Ξξ Xi Γγ Gamma Οο Omicron Δδ Delta Ππ Pi Εε Epsilon Ρρ Rho Ζζ Zeta Σσς Sigma Ηη Eta Ττ Tau Θθ Theta Υυ Upsilon Ιι Iota Φφ Phi Κκ Kappa Χχ Chi Λλ Lambda Ψψ Psi Μμ Mu Ωω Omega
History
Archaic local variants Ϝ Ͱ Ϻ Ϙ Ͳ Ͷ Diacritics Ligatures Numerals ϛ (6) ϟ (90) ϡ (900)
Use in other languages
Bactrian Coptic Albanian
Related topics
Use as scientific symbols
Category
v t e

Pi ( /ˈpaɪ/; Ancient Greek /piː/ or /peî/, uppercase Π, lowercase π, cursive ϖ; Greek: πι [pi]) is the sixteenth letter of the Greek alphabet, meaning units united, and representing the voiceless bilabial plosive IPA:  [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 Latin P, Cyrillic Pe (П, п), Coptic pi (Ⲡ, ⲡ), and Gothic pairthra (𐍀). ^[1]

Uppercase Pi

The uppercase letter Π is used as a symbol for:

• 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.

In science and engineering:

• 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.

Lowercase Pi

The lowercase letter π is used as a symbol 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).
• Often inflation rate in macroeconomics.
• Sometimes profit in microeconomics.
• 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 (in the earliest polyamory pride flag design, created by Jim Evans in 1995, pi stands for the first letter of polyamory). ^{[2] [3] [4] [5]}

History

An early form of pi was , appearing almost like a gamma with a hook.

Variant pi

Variant pi or "pomega" (${\displaystyle \varpi \,\!}$ or ϖ) is a glyph variant of lowercase pi sometimes used in technical contexts. It resembles a lowercase omega with a macron, though historically it is simply a cursive form of pi, with its legs bent inward to meet. It was also used in the minuscule script. It is a symbol for:

• Angular frequency of a wave in fluid dynamics (angular frequency is usually represented by ${\displaystyle \omega }$ but this may be confused with vorticity in a fluid dynamics context).
• Longitude of pericenter in celestial mechanics. ^[6]
• Comoving distance in cosmology. ^[7]
• Single-scattering albedo in radiative transfer.
• Mean fitness of a population in biology.
• Fundamental weights of a representation (probably to better distinguish from elements ${\displaystyle w}$ of the Weyl group, than the usual notation ${\displaystyle \omega }$).
• The lemniscate constant. ^[8]

Character encodings

The various forms of pi are present in Unicode as:

• U+03A0 Π GREEK CAPITAL LETTER PI (Π)
• U+03C0 π GREEK SMALL LETTER PI (π)
• U+03D6 ϖ GREEK PI SYMBOL (ϖ, ϖ)
• U+220F ∏ N-ARY PRODUCT (∏, ∏)
• U+1D28 ᴨ GREEK LETTER SMALL CAPITAL PI
• U+1D70B 𝜋 MATHEMATICAL ITALIC SMALL PI
• U+1D6D1 𝛑 MATHEMATICAL BOLD SMALL PI. ^[9]

Character encodings tables

See also

Look up Π or π in Wiktionary, the free dictionary.

• П, п – Pe (Cyrillic)
• P, p – Pe (Latin)
• Greek letters used in mathematics, science, and engineering#Ππ (pi)
• Tau

References