Beraha constants
# Beraha constants

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

    $B(n)=2+2\cos \left({\frac {2\pi }{n}}\right).$

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.

| $n$ | $B(n)$ | Approximately |
| - | - | - |
| 1 | 4 | |
| 2 | 0 | |
| 3 | 1 | |
| 4 | 2 | |
| 5 | ${\frac {1}{2}}(3+{\sqrt {5}})$ | 2.618 |
| 6 | 3 | |
| 7 | $2+2\cos({\tfrac {2}{7}}\pi )$ | 3.247 |
| 8 | $2+{\sqrt {2}}$ | 3.414 |
| 9 | $2+2\cos({\tfrac {2}{9}}\pi )$ | 3.532 |
| 10 | ${\frac {1}{2}}(5+{\sqrt {5}})$ | 3.618 |
