Journal ArticleDOI
A spigot algorithm for the digits of pi
Stanley Rabinowitz,Stan Wagon +1 more
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TLDR
It is remarkable that the algorithm illustrated in Table 1, which uses no floating-point arithmetic, produces the digits of π, which starts with some 2s in columns headed by the fractions shown.Abstract:
(1995). A Spigot Algorithm for the Digits of π. The American Mathematical Monthly: Vol. 102, No. 3, pp. 195-203.read more
Citations
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On the rapid computation of various polylogarithmic constants
TL;DR: These algorithms can be easily implemented, require virtually no memory, and feature run times that scale nearly linearly with the order of the digit desired make it feasible to compute the billionth binary digit of log(2) or π on a modest work station in a few hours run time.
Posted Content
On the rapid computation of various polylogarithmic constants
TL;DR: In this paper, the d-th digit of certain transcendental numbers in various bases was computed in a few hours run time, and the algorithm was shown to scale linearly with the order of the desired digit.
Journal ArticleDOI
The quest for PI
TL;DR: A brief history of the analysis and computation of the mathematical constant Pi = 3.14159 can be found in this paper, including a number of the formulas that have been used to compute Pi through the ages.
Journal ArticleDOI
Birth, growth and computation of pi to ten trillion digits
TL;DR: The universal real constant pi, the ratio of the circumference of any circle and its diameter, has no exact numerical representation in a finite number of digits in any number/radix system as mentioned in this paper.
Pokroky matematiky, fyziky a astronomie
TL;DR: Volf et al. as mentioned in this paper presented the results, achieved by representatives of the Czech Republic, of the 21st century European Union Science Olympiad (EUSO), which has not even reached ten years.
References
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Book
The Art of Computer Programming
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
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Ramanujan, modular equations, and approximations to Pi or how to compute one billion digits of Pi
TL;DR: The year 1987 was the centenary of Ramanujan's birth, which was the first year of modern algebraic manipulation software, such as MACSYMA as discussed by the authors, and it is possible to see how much more spectacular his already astonishing career might have been had he lived to have access to powerful algebraic manipulators.
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The Calculation of e to Many Significant Digits
TL;DR: The interesting problem of accurate evaluation of the number e is discussed, and a new technique proposed which evaluates the digits of e (in any base) in sequence is proposed.
Journal ArticleDOI
Algorithm 393: Special series summation with arbitrary precision
TL;DR: The present algorithm requires only integer arithmetic and can be implemented in any algebraic language and is applicable to series in which the ratios of successive terms can be expressed as quotients of given integers or integer functions of term positions.