Beraha Constants

The Beraha constants are a series of mathematical constants by which the $n\text$ Beraha constant is given by

: $B (n) = 2 + 2 \cos \left ( \frac \right ).$

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

The following table summarizes the first ten Beraha constants.

See also

* Chromatic polynomial

Notes

References

*
*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 $\lambda = 1$," Research Report COPR 72–7, University of Waterloo, 1972a.
*Tutte, W. T. "Chromatic Sums for Planar Triangulations IV: The Case $\lambda = \infty$." Research Report COPR 72–4, University of Waterloo, 1972b.

Mathematical constants

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