# Π

(Redirected from Pi)
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
• 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 ${\displaystyle (1-{\frac {1}{9}})^{2}}$, equivalent to taking a value of about 3.16 for ${\displaystyle \pi }$. The Babylonians adopted the cruder approximation 3... (although an instance is known in which the value is taken as ${\displaystyle 3{\frac {1}{8}}}$), 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.
• 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, ${\displaystyle e^{i\pi }+1=0.\,\!}$ 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
${\displaystyle {\frac {4}{\pi }}={\frac {3}{2}}\cdot {\frac {3}{4}}\cdot {\frac {5}{4}}\cdot {\frac {5}{6}}\cdot {\frac {7}{6}}\cdot {\frac {7}{8}}\cdots }$
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