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Download as PDF; Printable version; In other projects ... This category presents articles pertaining to the calculation of Pi to arbitrary precision. Pages in ...
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.
A variant of the spigot approach uses an algorithm which can be used to compute a single arbitrary digit of the transcendental without computing the preceding digits: an example is the Bailey–Borwein–Plouffe formula, a digit extraction algorithm for π which produces base 16 digits. The inevitable truncation of the underlying infinite ...
Using the P function mentioned above, the simplest known formula for π is for s = 1, but m > 1. Many now-discovered formulae are known for b as an exponent of 2 or 3 and m as an exponent of 2 or it some other factor-rich value, but where several of the terms of sequence A are zero.
The Gauss–Legendre algorithm is an algorithm to compute the digits of π. It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of π . However, it has some drawbacks (for example, it is computer memory -intensive) and therefore all record-breaking calculations for many years have used other ...
Borwein's algorithm was devised by Jonathan and Peter Borwein to calculate the value of /. This and other algorithms can be found in the book Pi and the AGM – A Study in Analytic Number Theory and Computational Complexity .
Once the message has been sent, becomes the process , while () becomes the process [/], which is with the place-holder substituted by , the data received on . The class of processes that P {\displaystyle {\mathit {P}}} is allowed to range over as the continuation of the output operation substantially influences the properties of the calculus.
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.