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The number π (/ p aɪ / ⓘ; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.
The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant pi (π). For more detailed explanations for some of these calculations, see Approximations of π. As of July 2024, π has been calculated to 202,112,290,000,000 (approximately 202 trillion) decimal digits.
where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.
An animated image showing the definition of pi.A number line is marked off by a circle of unit diameter.Starting from zero, the circle "unrolls" its circumference.At one full turn, the unrolled circumference has extended to the point we call π.
The software may be obtained from the Pi-Hacks Yahoo! forum, or from Stu's Pi page. Super PI by Kanada Laboratory [101] in the University of Tokyo is the program for Microsoft Windows for runs from 16,000 to 33,550,000 digits. It can compute one million digits in 40 minutes, two million digits in 90 minutes and four million digits in 220 ...
Estimating PI Visualization (Flash) Buffon's needle: fun and fundamentals (presentation) at slideshare; Animations for the Simulation of Buffon's Needle by Yihui Xie using the R package animation; 3D Physical Animation by Jeffrey Ventrella; Padilla, Tony. "π Pi and Buffon's Needle". Numberphile. Brady Haran. Archived from the original on 2013 ...
A History of Pi (book) Indiana Pi Bill; Leibniz formula for pi; Lindemann–Weierstrass theorem (Proof that π is transcendental) List of circle topics; List of formulae involving π; Liu Hui's π algorithm; Mathematical constant (sorted by continued fraction representation) Mathematical constants and functions; Method of exhaustion; Milü; Pi ...
Piphilology comprises the creation and use of mnemonic techniques to remember many digits of the mathematical constant π.The word is a play on the word "pi" itself and of the linguistic field of philology.