Pi (letter)

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 Diacritics Ligatures Numerals ϛ (6) ϟ (90) ϡ (900)
Use in other languages
Bactrian Coptic Albanian
Related topics
Use as scientific symbols
Book Category

Pi (; Greek: , uppercase Π, lowercase π) is the sixteenth letter of the Greek alphabet, representing [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 (П, п), Coptic pi (Ⲡ, ⲡ), and Gothic pairthra (𐍀).

Symbol

The upper-case letter Π is used as a symbol for:

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

The lower-case letter π is used as a symbol for:

• The mathematical real transcendental (and thus irrational) constant π ≈ 3.1415926535897932384626433832795028841971…, 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 pi meson or pion.
• 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.
• In reinforcement learning π denotes policy.

History

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

In the book 'L'alphabet grec', T. H. de Mortain speculates that letter П is a gate, since it is the first letter of "πύλη" (gate of town or temple). Allegedly, the Greeks wanted to represent the shape of the entrance to civilization, such as the gate of the lions in Mycenae. This hypothesis is not shared by any other authority in the field and has no other attestation.

Variant pi

Variant pi or "pomega" (\varpi\,\! or ϖ) is a glyph variant of lower case pi sometimes used in technical contexts as though it were a lower-case omega with a macron, though historically it is simply a cursive form of pi, with its legs bent inward to meet. It is used as a symbol for:

• Angular frequency of a wave, in fluid dynamics (angular frequency is usually represented by \omega but this may be confused with vorticity in a fluid dynamics context).
• Longitude of pericenter, in celestial mechanics.^[1]
• Comoving distance in cosmology.^[2]
• Single-scattering albedo in Radiative transfer.

The various forms of pi are present in Unicode as:

• U+03A0 Π greek capital letter pi (HTML Π · Π)
• U+03C0 π greek small letter pi (HTML π · π)
• U+03D6 ϖ greek pi symbol (HTML ϖ · ϖ)
• U+220F ∏ n-ary product (HTML ∏ · ∏)
• U+1D28 ᴨ greek letter small capital pi (HTML ᴨ)
• U+1D70B 휋 mathematical italic small pi (HTML 𝜋)
• U+1D6D1 훑 mathematical bold small pi (HTML 𝛑).^[3]

Character Encodings

• Greek / Coptic Pi^[4]

• Mathematical Pi

These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

See also

• П, п - Pe (Cyrillic)
• Р, р - Er (Cyrillic)
• P, p - Pe (Latin)
• Greek letters used in mathematics, science, and engineering#Ππ (pi)

References