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The Chudnovsky algorithm is a fast method for calculating the digits of π, based on Ramanujan's π formulae.Published by the Chudnovsky brothers in 1988, [1] it was used to calculate π to a billion decimal places.
Scott's pi (named after William A Scott) is a statistic for measuring inter-rater reliability for nominal data in communication studies.Textual entities are annotated with categories by different annotators, and various measures are used to assess the extent of agreement between the annotators, one of which is Scott's pi.
In mathematics, Machin-like formulas are a popular technique for computing π (the ratio of the circumference to the diameter of a circle) to a large number of digits.They are generalizations of John Machin's formula from 1706:
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.
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To calculate 16 n−k mod (8k + 1) quickly and efficiently, the modular exponentiation algorithm is done at the same loop level, not nested. When its running 16x product becomes greater than one, the modulus is taken, just as for the running total in each sum. Now to complete the calculation, this must be applied to each of the four sums in turn.
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.
is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler . It is a special case of Euler's formula e i x = cos x + i sin x {\displaystyle e^{ix}=\cos x+i\sin x} when evaluated for x = π {\displaystyle x=\pi } .