Metallic Numbers

For all the fame and attention that the Golden Ratio ($\phi \approx 1.618$) gets in comparison to the rest of the mathematical constants, there is a whole family of constants which get left out of the picture.

It is relatively common to know that $\phi$ can be represented with an algebraic representation: $\frac{1 + \sqrt{5}}{2}=\phi.$ But that expression generalizes to the rest of the integers!

$$\frac{n + \sqrt{n^2+4}}{2} \quad \forall n\in \N$$

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