Abstract
In a series of five papers we presented some
fundamental knowledge about hyperbolic functions and 184 properties expressed
in 193 equalities. After in a previous paper, using hyperbolic functions, we
showed that there is a field of real functions of real variable isomorphic with
the field of real numbers in this paper we will present a study of Fibonacci
and Lucas sequences, with the help of these functions. Thus, starting from the
definition recurrence relations of the
Fibonacci and Lucas sequences, we will list here 18 relations between the
hyperbolic functions and these sequences, followed by 12 consequences of them, 12
relations between the terms of the Fibonacci and Lucas sequences. All these relationships
will be fully proven, moreover, some will be proven in two ways.
