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Beraha constants

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The Beraha constants are a series of mathematical constants by which the Beraha constant is given by

Notable examples of Beraha constants include is , where is the golden ratio, is the silver constant[1] (also known as the silver root),[2] and .

The following table summarizes the first ten Beraha constants.

Approximately
1 4
2 0
3 1
4 2
5 2.618
6 3
7 3.247
8 3.414
9 3.532
10 3.618

See also

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Notes

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  1. ^ Weisstein, Eric W. "Silver Constant". Wolfram MathWorld. Retrieved November 3, 2018.
  2. ^ Weisstein, Eric W. "Silver Root". Wolfram MathWorld. Retrieved May 5, 2020.

References

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  • Weisstein, Eric W. "Beraha Constants". Wolfram MathWorld. Retrieved November 3, 2018.
  • Beraha, S. Ph.D. thesis. Baltimore, MD: Johns Hopkins University, 1974.
  • Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 143, 1983.
  • Saaty, T. L. and Kainen, P. C. The Four-Color Problem: Assaults and Conquest. New York: Dover, pp. 160–163, 1986.
  • Tutte, W. T. "Chromials." University of Waterloo, 1971.
  • Tutte, W. T. "More about Chromatic Polynomials and the Golden Ratio." In Combinatorial Structures and their Applications: Proc. Calgary Internat. Conf., Calgary, Alberta, 1969. New York: Gordon and Breach, p. 439, 1969.
  • Tutte, W. T. "Chromatic Sums for Planar Triangulations I: The Case ," Research Report COPR 72–7, University of Waterloo, 1972a.
  • Tutte, W. T. "Chromatic Sums for Planar Triangulations IV: The Case ." Research Report COPR 72–4, University of Waterloo, 1972b.