Draft:Bronze Ratio

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The bronze ratio is a ratio in mathematics where 3 times a larger quantity plus the smaller quantity, divided by the larger quantity, is equal to the larger quantity divided by the smaller quantity. Its value is equal to ⁠3+√13/2⁠

and is the third metallic mean, approximately equal to 3.30277563773...^[1][2] The mean/ratio is usually denoted with the symbol β, or with the symbol μ but it usually varies and there is no standard symbol

We can denote the relation of this ratio algebraically as:

${\displaystyle {\frac {3x+y}{x}}={\frac {x}{y}}\equiv \beta }$

Using the continued fraction that all metallic means follow of, [n; n, n, n, ...]: the bronze ratio can be expressed as:

${\displaystyle 3+{\cfrac {1}{3+{\cfrac {1}{3+{\cfrac {1}{3+\ddots }}}}}}=\beta }$