## Abstract

The nature of the number π has intrigued mathematicians since the beginning of mathematical history. The most important properties of π are its irrationality and transcendence, which were established in 1761 and 1882, respectively. In the twentieth century the focus has been on a different sort of question, namely whether π, despite being irrational and transcendental, is normal.

## Keywords

Decimal Place Decimal Expansion Mathematical History Poker Hand Poker Test
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## References

- J. M. Borwein and P. B. Borwein, The arithmetic-geometric mean and fast computation of elementary functions,
*SIAM Review*26, (1984) 351–366.CrossRefMATHMathSciNetGoogle Scholar - R. P. Brent, Multiple-precision zero-findings methods and the complexity of elementary function evaluation, in
*Analytic Computational Complexity*, J. F. Traub, ed., New York: Academic Press, 1976, pp. 151–176.Google Scholar - D. Cox, The arithmetic-geometric mean of Gauss,
*Ens. Math. 30*, (1984) 275–330.MATHGoogle Scholar - G. H. Hardy and E. M. Wright,
*An Introduction to the Theory of Numbers*, 4th edition, London: Oxford, 1975.Google Scholar - Y. Kanada, Y. Tamura, S. Yoshino, and Y. Ushiro, Calculation of π to 10,013,395 decimal places based on the Gauss-Legendre algorithm and Gauss arctangent relations,
*Mathematics of Computation*(forthcoming).Google Scholar - D. E. Knuth,
*The Art of Computer Programming*, vol. 2, Reading, Mass.: Addison-Wesley, 1969.MATHGoogle Scholar - I. Niven,
*Irrational Numbers*, Carus Mathematical Monographs, No. 11, The Mathematical Association of America. Distributed by Wiley, New York, 1967.Google Scholar - E. Salamin, Computation of π using arithmetic-geometric mean,
*Mathematics of Computation 30*, (1976) 565–570.MATHMathSciNetGoogle Scholar

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© Springer Science+Business Media New York 2004