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Pi

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This is a disambiguation page: a list of articles associated with the same title. If you arrived here from another page, you may wish to go back to that page and change the link to point directly to the intended article.

Pi, the 16th Greek letter, lowercase π, uppercase Π, can refer to:

  • pi (constant) - π ≈ 3.141592653589793238462643383279502884197169399375105820974944592307816406286208..., an irrational number representing the ratio of a circle's circumference to its diameter (also known as Archimedes' number)
  • Product operator Π — e.g., \prod_{i=0}^n f(i). (See also product of a sequence.) It is functionally similar to summation notation, using \sum_{i=0}^n, which is the sum of a sequence.
  • Prime counting function π(x). (See also prime numbers.) A function defined to return a value equal to the quantity of prime numbers less than or equal to its inputted value. (eg \pi(8) = 4 since only four numbers: 2,3,5,7 are all the prime numbers less than or equal to 8.)
  • The transformation (horizontal shift) of the Gamma function: \Pi(x) = \Gamma(x+1).
    • The reciprocal of its capitalized counterpart: \pi(x) =\frac{1}{\Pi(x)}.
  • The upside down capital represent Coproducts: \coprod_{j \in J}

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