Geodesic
On the general theory of hyperbolic functions based on the hyperbolic Fibonacci and Lucas functions and on Hilbert's Fourth Problem
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},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_2013_15_1_a3/}
}
TY  - JOUR
AU  - Alexey Stakhov
TI  - On the general theory of hyperbolic functions based on the hyperbolic Fibonacci and Lucas functions and on Hilbert's Fourth Problem
JO  - Visual Mathematics
PY  - 2013
VL  - 15
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VM_2013_15_1_a3/
LA  - en
ID  - VM_2013_15_1_a3
ER  - 
%0 Journal Article
%A Alexey Stakhov
%T On the general theory of hyperbolic functions based on the hyperbolic Fibonacci and Lucas functions and on Hilbert's Fourth Problem
%J Visual Mathematics
%D 2013
%V 15
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VM_2013_15_1_a3/
%G en
%F VM_2013_15_1_a3
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/