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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:

Related Definitions

• Greek Alphabet
• Greek Numerals

Sources

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