Beraha constants

Short description: Mathematical constants

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

B(n)=2+2cos⁡(2πn).

Notable examples of Beraha constants include B(5)is φ+1, where φ is the golden ratio, B(7)is the silver constant[1] (also known as the silver root),[2] and B(10)=φ+2.

The following table summarizes the first ten Beraha constants.

n | B(n) | Approximately

|
|

1  | 4  |
2  | 0  |
3  | 1  |
4  | 2  |
5  | 12(3+5) | 2.618
6  | 3  |
7  | 2+2cos⁡(27π) | 3.247
8  | 2+2 | 3.414
9  | 2+2cos⁡(29π) | 3.532
10  | 12(5+5) | 3.618

## See also

* Chromatic polynomial

## Notes

1. ↑ Weisstein, Eric W.. "Silver Constant". http://mathworld.wolfram.com/SilverConstant.html.
2. ↑ Weisstein, Eric W.. "Silver Root". http://mathworld.wolfram.com/SilverRoot.html.

## References

* Weisstein, Eric W.. "Beraha Constants". http://mathworld.wolfram.com/BerahaConstants.html.
* 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 λ=1," Research Report COPR 72–7, University of Waterloo, 1972a.
* Tutte, W. T. "Chromatic Sums for Planar Triangulations IV: The Case λ=∞." Research Report COPR 72–4, University of Waterloo, 1972b.

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