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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.
In mathematics, the Leibniz formula for π, named after Gottfried Wilhelm Leibniz, states that = + + = = +,. an alternating series.. It is sometimes called the Madhava–Leibniz series as it was first discovered by the Indian mathematician Madhava of Sangamagrama or his followers in the 14th–15th century (see Madhava series), [1] and was later independently rediscovered by James Gregory in ...
More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...
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.
John Wallis, English mathematician who is given partial credit for the development of infinitesimal calculus and pi. Viète's formula, a different infinite product formula for . Leibniz formula for π, an infinite sum that can be converted into an infinite Euler product for π. Wallis sieve
This category includes articles related to the mathematical constant pi (π), which represents the ratio of a circle's circumference to its diameter. For other uses, see Pi (disambiguation) . The main article for this category is Pi .
Download QR code; Print/export Download as PDF; Printable version; ... In mathematics, at least four different functions are known as the pi or Pi function:
In the 1760s, Johann Heinrich Lambert was the first to prove that the number π is irrational, meaning it cannot be expressed as a fraction /, where and are both integers. ...