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 (also known as the silver root and Tutte–Beraha constant), 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[edit]
References[edit]
- ^ Weisstein, Eric W. "Beraha Constants". Wolfram MathWorld. Retrieved November 3, 2018.
- ^ Weisstein, Eric W. "Silver Constant". 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.