Pi

How to read it

Dictionary.com and the Collins English Dictionary both give the pronunciation /paɪ/, the same as “pie”. Collins describes pi as a consonant, transliterated as p.

Also searched as: pi letter, pi symbol, π, Π, π meaning.

Capital and small forms

Unicode describes ϖ as a technical symbol, a variant of pi that looks like Omega; NIST’s guide to the SI lists it as a second italic form of π. The product sign ∏ is a separate character from the letter Π, as the summation sign ∑ is from Sigma.

Pi in maths

The small π is the ratio of the circumference of a circle to its diameter, 3.14159 26535 89793 23846… (NIST DLMF §3.12); Unicode’s own chart notes it as the “math constant 3.141592...”. The capital shape, as the product sign ∏, stands for a product of terms, as ∑ does for a sum. In number theory π(x) is a function, not the constant: the number of primes not exceeding x (DLMF §27.2).

In AI and machine learning

In reinforcement learning π is a policy, the rule an agent uses to decide what actions to take. OpenAI’s Spinning Up guide writes a stochastic policy as π and a deterministic one as μ.

In quantum physics

The reduced Planck constant ħ is Planck’s constant divided by 2π: Unicode names the character ℏ “PLANCK CONSTANT OVER TWO PI” (see Psi). In particle physics π is the pion, a meson: OpenStax lists π⁺ and π⁻ at 139.6 MeV, and the neutral π⁰ is its own antiparticle.