# Π

ratio of the circumference of a circle to its diameter

**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.

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## QuotesEdit

- Historically [analytic geometry] arose... from the comparison of curvilinear and rectilinear magnitudes. ...the Egyptians and Babylonians, in their geometry of the circle, took the first steps. The former made a remarkably accurate estimate of the ratio of the area of the circle to the area of the square on the diameter, taking the ratio to be , equivalent to taking a value of about 3.16 for . The Babylonians adopted the cruder approximation 3... (although an instance is known in which the value is taken as ), but... recognized that the angle inscribed in a semicircle is right, anticipating Thales by well over a thousand years. Moreover, they were familiar... with the Pythagorean theorem.
- Carl B. Boyer,
*History of Analytic Geometry*(1956)

- Carl B. Boyer,

**Sweet and gentle and sensitive man**

With an obsessive nature and deep fascination

For numbers

And a complete infatuation with the calculation

Of π.

- 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...

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

- Maximillian Cohen, in

**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

- Maximillian Cohen, in

**One of the most frequently mentioned equations was Euler's equation, 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.

- There is a famous formula, perhaps the most compact and famous of all formulas — developed by Euler from a discovery of de Moivre:
**It appeals equally to the mystic, the scientist, the philosopher, the mathematician.**- Edward Kasner and James R. Newman in
*Mathematics and the Imagination*(1940)

- Edward Kasner and James R. Newman in

**Among his**[John Wallis']**interesting discoveries was**the relation

**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

- David Eugene Smith,