Pi (Greek: π / piː/ or /peî/; uppercase Π, lowercase π, cursive ϖ) is the sixteenth letter of the Greek alphabet. In Classical Greek it denoted the voiceless bilabial plosive /p/. In the system of Greek numerals the letter has the value 80.
Etymology and development
Pi derives from the Phoenician letter Pe, which represented the sound /p/. Through the Greek adaptation of the Phoenician script, Pe evolved into the form Π/π. Descendant letters in later alphabets include Latin P, Cyrillic П (Pe), Coptic Ⲡ (π), and Gothic 𐍀 (pairthra).
Phonetic value
In both Ancient and Modern Greek the letter corresponds to the phoneme /p/. Its pronunciation in English varies between “pie” (/paɪ/) and “pee” (/piː/), reflecting different scholarly conventions.
Mathematical and scientific symbols
Uppercase Π
- Represents the product operator (Π‑notation), analogous to the summation symbol Σ.
- Used in textual criticism to denote the Codex Petropolitanus.
- Serves as a shorthand for “plaintiff” in legal notation.
- Denotes a portfolio in mathematical finance.
- Symbolises osmotic pressure in chemistry and the viscous stress tensor in continuum mechanics.
Lowercase π
- Denotes the transcendental constant π ≈ 3.14159…, the ratio of a circle’s circumference to its diameter in Euclidean geometry.
- Represents the prime‑counting function π(x), which counts the number of primes ≤ x.
- Appears in algebraic topology as the notation for homotopy groups πₙ.
- Functions in dimensional analysis via the Buckingham π theorem.
- Indicates a pi bond, the type of covalent bond formed by side‑by‑side overlap of p‑orbitals.
- Used for the projection map on a tangent bundle, for projection in relational algebra, and for policy functions in reinforcement learning.
- Occasionally stands for the inflation rate in macroeconomics or for profit in microeconomics.
Cultural references
The lowercase π has been employed as a symbol for polyamory, appearing on early polyamory pride flags because it is the first letter of the Greek words περιφέρεια (periphery) and περίμετρος (perimeter).
Numerical value
In Greek numeral notation Π/π corresponds to the value 80.
Related characters
- Latin P (derived)
- Cyrillic П (Pe)
- Coptic Ⲡ / ⲡ (pi)
- Gothic 𐍀 (pairthra)
The letter Pi continues to be a ubiquitous symbol across mathematics, science, engineering, law, and cultural contexts.
