Geodesic
On the general theory of hyperbolic functions based on the hyperbolic Fibonacci and Lucas functions and on Hilbert's Fourth Problem
Visual Mathematics, Tome 15 (2013) no. 1 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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The article is devoted to description of the new classes of hyperbolic functions based on the "golden" ratio and "metallic proportions," what leads to the general theory of hyperbolic functions. This theory resulted in the original solution of Hilbert's Fourth Problem and puts in front to theoretical natural sciences a challenge to search new "hyperbolic worlds" of Nature.
Classification : 20H15 
@article{VM_2013_15_1_a3,
     author = {Alexey Stakhov},
     title = {On the general theory of hyperbolic functions based on the hyperbolic {Fibonacci} and {Lucas} functions and on {Hilbert's} {Fourth} {Problem}},
     journal = {Visual Mathematics},
     year = {2013},
     volume = {15},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_2013_15_1_a3/}
}
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Alexey Stakhov. On the general theory of hyperbolic functions based on the hyperbolic Fibonacci and Lucas functions and on Hilbert's Fourth Problem. Visual Mathematics, Tome 15 (2013) no. 1. http://geodesic.mathdoc.fr/item/VM_2013_15_1_a3/