# Π

Something's going on. It has to do with that number. There's an answer in that number. ~ π
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 a transcendental number, approximately equal to 3.14159265358979 in the usual decimal notation.

## Quotes

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
• 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...
• Something's going on. It has to do with that number. There's an answer in that number.
• 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.
• Among his [John Wallis'] interesting discoveries was the relation
$\frac{4}{\pi} = \frac32\cdot\frac34\cdot\frac54\cdot\frac56\cdot\frac76\cdot\frac78\cdots$
one of the early values of π involving infinite products.
• David Eugene Smith, History of Mathematics (1923) Vol.1; Footnote: see his Opera Mathematica, I, 441