Most people have heard of the golden ratio, but have you ever heard of the silver ratio? I only heard of it this week. The golden ratio can be expressed by a continued fraction in which all coefficients equal 1.
The silver ratio is the analogous continued fraction with all coefficients equal to 2.
You might think for a moment that the silver ratio should be just twice the golden ratio, but the coefficients contribute to the series in a non-linear way. The silver ratio actually equals 1 + √2. The golden ratio has a simple geometric interpretation. I don’t know of a geometric interpretation of the silver ratio. (Update: See Maxwell’s Demon for geometric applications of the silver ratio.)