Geodesic
The Golden Section, Fibonacci Series and New Hyperbolic Models of Nature
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.
Classification : 11B39 51M10
Keywords: The Golden Section, Fibonacci and Lucas numbers, Binet formulas, the Golden Shofar, hyperbolic functions, Dichotomy principle, the Golden Section principle. 
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     author = {Alexey Stakhov and Boris Rozin},
     title = {The {Golden} {Section,} {Fibonacci} {Series} and {New} {Hyperbolic} {Models} of {Nature}},
     journal = {Visual Mathematics},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_2006_8_3_a3/}
}
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Alexey Stakhov; Boris Rozin. The Golden Section, Fibonacci Series and New Hyperbolic Models of Nature. Visual Mathematics, Tome 8 (2006) no. 3. http://geodesic.mathdoc.fr/item/VM_2006_8_3_a3/