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Is π Normal?

  • Stan Wagon

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 Massachusetts 01063 Mathematical History Poker Hand 
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References

  1. J. M. Borwein and P. B. Borwein, The arithmetic-geometric mean and fast computation of elementary functions, SIAM Review 26, (1984) 351–366.MathSciNetMATHCrossRefGoogle Scholar
  2. 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
  3. D. Cox, The arithmetic-geometric mean of Gauss, Ens. Math. 30, (1984) 275–330.MATHGoogle Scholar
  4. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th edition, London: Oxford, 1975.Google Scholar
  5. Y. Kanada, Y. Tamura, S. Yoshino, and Y. Ushiro, Calculation of Tr to 10,013,395 decimal places based on the Gauss-Legendre algorithm and Gauss arctangent relations, Mathematics of Computation (forthcoming).Google Scholar
  6. D. E. Knuth, The Art of Computer Programming, vol. 2, Reading, Mass.: Addison-Wesley, 1969.Google Scholar
  7. L Niven, Irrational Numbers, Carus Mathematical Monographs, No. 11, The Mathematical Association of America. Distributed by Wiley, New York, 1967.Google Scholar
  8. E. Salamin, Computation of IT using arithmetic-geometric mean, Mathematics of Computation 30, (1976) 565–570.MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Stan Wagon
    • 1
  1. 1.Department of MathematicsSmith CollegeNorthamptonUSA

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