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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.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
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.
It can be seen that as N gets larger (1 + iπ / N ) N approaches a limit of −1. Euler's identity asserts that e i π {\displaystyle e^{i\pi }} is equal to −1. The expression e i π {\displaystyle e^{i\pi }} is a special case of the expression e z {\displaystyle e^{z}} , where z is any complex number .
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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.
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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.