The Golden Section, Fibonacci Series and New Hyperbolic Models of Nature

Alexey Stakhov, Boris Rozin

A survey of new mathematical models of Nature is presented based on the Golden Section and using a class of hyperbolic Fibonacci and Lucas functions, and a surface referred to as the Golden Shofar. Also considered afre generalized Fibonacci numbers, generalized golden proportions, a Generalized Principle of the Golden Section, golden algebraic equations, generalized Binet formulas, generalized Lucas numbers, continuous functions for the generalized Fibonacci and Lucas numbers, Fibonacci matrices, and golden matrices.