Pi

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`Pi`

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is , with numerical value .

Details

Mathematical constant treated as numeric by NumericQ and as a constant by D.
Pi can be evaluated to any numerical precision using N.
Pi can be entered in StandardForm and InputForm as π, pi, p or \[Pi].
In StandardForm, Pi is printed as π.

Background & Context

Pi is the symbol representing the mathematical constant , which can also be input as ∖[Pi]. Pi is defined as the ratio of the circumference of a circle to its diameter and has numerical value . Pi arises in many mathematical computations including trigonometric expressions, special function values, sums, products, and integrals as well as in formulas from a wide range of mathematical and scientific fields.
When Pi is used as a symbol, it is propagated as an exact quantity. While many expressions involving Pi (e.g. Cos[Pi/10]) are automatically expanded in terms of simpler functions, expansion and simplification of more complicated expressions involving Pi (e.g. Cos[Pi/15]) may require use of functions such as FunctionExpand and FullSimplify.
Pi is known to be both irrational and transcendental, meaning it can be expressed neither as a ratio of integers nor as the root of any integer polynomial. While it is not known if Pi is normal (meaning the digits in its base- expansion are equally distributed) to any base, its known digits are very uniformly distributed.
Pi can be evaluated to arbitrary numerical precision by means of the Chudnovsky formula using N. In fact, calculating the first million decimal digits of Pi takes only a fraction of a second on a modern desktop computer. RealDigits can be used to return a list of digits of Pi and ContinuedFraction to obtain terms of its continued fraction expansion.
Most angle-related functions in the Wolfram Language take radian measures as their arguments and return radian measures as results. The symbol Degree, which is equal to Pi/180, can therefore be used as a multiplier when entering values in degree measures (e.g. Cos[30 Degree]).