π

Something's going on. It has to do with thatnumber.There's an answer in that number. ~π

Sweetandgentleandsensitiveman
With an obsessivenatureand deep fascination
Fornumbers
And acompleteinfatuation with thecalculation
Of π.... ~Kate Bush

π(sometimes writtenpi) is amathematicalconstant whosevalueis the ratio of anycircle's circumference to its diameter inEuclidean space;this is the same value as the ratio of a circle's area to the square of its radius. π is atranscendental number,approximately equal to 3.14159265358979 in the usual decimal notation.

Quotes

He doeslovehisnumbers
And they run, they run, they run him
In a great bigcircle
In a circle ofinfinity... ~Kate Bush

• There is a close and beautiful connection between the transformation theory forelliptic integralsand the very rapid approximation of pi. This connection was first made explicit byRamanujanin 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$(1-{\frac {1}{9}})^{2}$,equivalent to taking a value of about 3.16 for$\pi$.The Babylonians adopted the cruder approximation 3... (although an instance is known in which the value is taken as$3{\frac {1}{8}}$), but... recognized that the angle inscribed in a semicircle is right, anticipatingThalesby well over a thousand years. Moreover, they were familiar... with thePythagorean theorem.
  • Carl B. Boyer,History of Analytic Geometry(1956)

• We all know that π = 3.14159 and little kids can sometimes give it out to hundreds of decimal places. But thestock marketis 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)

• Sweetandgentleandsensitiveman
  With an obsessivenatureand deep fascination
  Fornumbers
  And acompleteinfatuation with thecalculation
  Of π.
  • Kate Bush,inAerial(2005) Disc I:A Sea of Honey

• He doeslovehisnumbers
  And they run, they run, they run him
  In a great bigcircle
  In a circle ofinfinity
  3.14159 26535897932 3846 264 338 3279...
  • Kate Bush,inAerial(2005) Disc I:A Sea of Honey

• It's adoor,Sol. It's a door.
  • Maximillian Cohen, inπ(1998),written byDarren 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, inπ(1998),written byDarren Aronofsky,Sean Gullette, and Eric Watson

• One of the most frequently mentioned equations wasEuler's equation,$e^{i\pi }+1=0.\,\!$Respondents called it "the most profound mathematical statement ever written"; "uncanny and sublime"; "filled withcosmicbeauty";and"mind-blowing ".Another asked: "What could be moremysticalthan an imaginary number interacting withrealnumbers to producenothing?"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 afamousformula, perhaps the most compact and famous of all formulas — developed byEulerfrom a discovery ofde Moivre:$e^{i\pi }+1=0.\,\!$It appeals equally to themystic,thescientist,thephilosopher,themathematician.
  • Edward KasnerandJames R. NewmaninMathematics and the Imagination(1940)

• Among his[John Wallis']interesting discoveries wasthe relation
  ${\frac {4}{\pi }}={\frac {3}{2}}\cdot {\frac {3}{4}}\cdot {\frac {5}{4}}\cdot {\frac {5}{6}}\cdot {\frac {7}{6}}\cdot {\frac {7}{8}}\cdots$
  one of the early values ofπinvolving infinite products.
  • David Eugene Smith,History of Mathematics(1923) Vol.1; Footnote: see hisOpera Mathematica,I, 441

External links

• Digits of PiatDMOZ

π Day

• Exploratorium's Pi Day Web Site
• 10 pi facts for the most irrational Pi Day of your life (2015)
• NPR provides a "Pi Rap" audiovideo
• Pi Day
• Professor Lesser's Pi Day page
• Pi Day in France