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The number π (/ p aɪ /; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulae across mathematics and physics .
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.
[4] Until the 20th century, the number of digits of pi which mathematicians had the stamina to calculate by hand remained in the hundreds, so that memorization of all known digits at the time was possible. [5] In 1949 a computer was used to calculate π to 2,000 places, presenting one of the earliest opportunities for a more difficult challenge.
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The constant π (pi) has a natural definition in Euclidean geometry as the ratio between the circumference and diameter of a circle. It may be found in many other places in mathematics: for example, the Gaussian integral, the complex roots of unity, and Cauchy distributions in probability. However, its ubiquity is not limited to pure mathematics.
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables . is the radius,
(Pi function) – the gamma function when offset to coincide with the factorial Rectangular function π ( n ) {\displaystyle \pi (n)\,\!} – the Pisano period
IBM System/4 Pi, a family of avionics computers 4Pi microscope , a microscope that uses interference and fluorescence computers 4×π = 12.56637..., the solid angle of a complete sphere measured in steradians