The golden ratio revisited (Q2710511)

Much has been written about the golden ratio \(g={1+\sqrt 5\over 2}\). Its connections include classical architecture, population theory (especially rabbits), and the Fibonacci numbers \(f_n={1\over\sqrt 5}(g^n-g^{-n})\). The ring of integers of the field \({\mathbb{Q}}(\sqrt 5)\), generated by \(g\), provides a concrete field for demonstrating some of the concepts of algebraic number theory without tears or other complications. The associated recurrences, like \(f_n\) and the Lucas numbers \(V_n=g^n+g^{-n}\) figure in some classical tests for primality. The author provides a glimpse of all of this and more on his visit.