New Smarandache Sequences: the Family of Metallic Means

The family of Metallic Means comprises every quadratic irrational number that is the positive solution of algebraic equations of the types r--nx-l =0 and r--x-n =0 , where n is a natural number. The most prominent member of this family is the Golden Mean, then it comes the Silver Mean, the Bronze Mean, the NIckel Mean, the Copper Mean, etc. All of them are closely related to quasi-periodic dynamics, being therefore important clues in the study of the onset to chaos. However, they also constitute the basis of musical and architectural proportions. Through the analysis of their common mathematical properties, it becomes evident that they interconnect different human fiels of knowledge, in the sense defined by Florentin Smarandache ("Paradoxist Mathematics''). , Kevwords: continued fractions, quadratic irrationals, Fibonacci sequences, Smarandache sequences, hyperbolic map.