International Journal of

Arts , Humanities & Social Science

ISSN 2693-2547 (Print) , ISSN 2693-2555 (Online)
Study of Fibonacci and Lucas Sequences With the Help of Hyperbolic Functions


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.