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 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

• 100 plus 4, multiplied by 8, and added to 62,000: this is the nearly approximate measure of the circumference of a circle whose diameter is 20,000.
  • Aryabhata, in his work Ganitapada 10. According to the verse, Aryabhata’s value of π equals ((100+4)×8 + 62000)/20000, which is 3.1416.
  • quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189

• There is a close and beautiful connection between the transformation theory for elliptic integrals and the very rapid approximation of pi. This connection was first made explicit by Ramanujan in his 1914 paper " Modular Equations and Approximations to π " ....
  • Jonathan M. Borwein, Peter B. Borwein, and David H. Bailey, "Ramanujan, modular equations, and approximations to pi or how to compute one billion digits of pi." The American Mathematical Monthly 96, no. 3 (1989): 201–219.

• 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)

• Maths is really hard to define. ...Except I like to define maths as this
  This formula, which links to the odd numbers... It's true. It's always been there. It's absolutely wonderful. It connects odd numbers to the ratio of a circle, and... if you don't like that, then you have no mathematical soul.
  • Christopher Budd, "What Have Mathematicians Done for Us" (2016) from Gresham College Mathematical Lecture Series or Geometry Lecture Series. A YouTube video source: 3:43-4:43 (Posted Dec 1, 2016).

• We all know that π = 3.14159 and little kids can sometimes give it out to hundreds of decimal places. But the stock market is not like that. There's a range of reasonableness ...
  • Warren Buffett, (October 7, 2014) "Warren Buffett On Investment Strategy | Full Interview Fortune MPW". Fortune Magazine, YouTube. (quote at 7:46 of 38:17)

• 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

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

• 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

• 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.
  • 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: It appeals equally to the mystic, the scientist, the philosopher, the mathematician.
  • Edward Kasner and James R. Newman in Mathematics and the Imagination (1940)

• 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

External links

• Digits of Pi at DMOZ