π

Something's going on. It has to do with that number. There's an answer in that number. ~ "Maximillian Cohen"

It's a door, Sol. It's a door. ~ "Maximillian Cohen"

Sweet and gentle and sensitive man
With an obsessive nature and deep fascination
For numbers
And a complete infatuation with the calculation
Of π.... ~ Kate Bush

π (sometimes written pi) is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean space; this is the same value as the ratio of a circle's area to the square of its radius. π is an irrational number, approximately equal to 3.14159265358979 in the usual decimal notation; also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can be equal to its value. Also known as Archimedes Constant, it is one of the most important mathematical and physical constants, and many formulae from mathematics, science, and engineering involve it. The Greek letter π, often spelled out pi in text, was adopted for the number from the Greek word for perimeter "περίμετρος", first by William Jones in 1707, and popularized by Leonhard Euler in 1737.

Sourced

He does love his numbers
And they run, they run, they run him
In a great big circle
In a circle of infinity... ~ Kate Bush

• Something's going on. It has to do with that number. There's an answer in that number.
  • Maximillian Cohen, in π (1998), written by Darren Aronofsky, Sean Gullette, and Eric Watson.

• It's a door, Sol. It's a door.
  • Maximillian Cohen, in π (1998), written by Darren Aronofsky, Sean Gullette, and Eric Watson.

• Sweet and gentle and sensitive man
  With an obsessive nature and deep fascination
  For numbers
  And a complete infatuation with the calculation
  Of π.
  • Kate Bush, in Aerial (2005) Disc I : A Sea of Honey

• He does love his numbers
  And they run, they run, they run him
  In a great big circle
  In a circle of infinity
  3.14159 26535897932 3846 264 338 3279...
  • Kate Bush, in Aerial (2005) Disc I : A Sea of Honey

• One of the most frequently mentioned equations was Euler's equation, $e^{i \pi} + 1 = 0. \,\!$ Respondents called it "the most profound mathematical statement ever written"; "uncanny and sublime"; "filled with cosmic beauty"; and "mind-blowing". Another asked: "What could be more mystical than an imaginary number interacting with real numbers to produce nothing?" The equation contains nine basic concepts of mathematics — once and only once — in a single expression. These are: e (the base of natural logarithms); the exponent operation; π; plus (or minus, depending on how you write it); multiplication; imaginary numbers; equals; one; and zero.
  • Robert P. Crease, in "The greatest equations ever" at PhysicsWeb (October 2004)

• There is a famous formula, perhaps the most compact and famous of all formulas — developed by Euler from a discovery of de Moivre: $e^{i \pi} + 1 = 0. \,\!$ It appeals equally to the mystic, the scientist, the philosopher, the mathematician.
  • Edward Kasner and James R. Newman in Mathematics and the Imagination (1940).