On the golden number and Fibonacci type sequences

Eugeniusz Barcz. "On the golden number and Fibonacci type sequences." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 11 (2019): 25-35. <http://eudml.org/doc/296320>.

@article{EugeniuszBarcz2019,
abstract = {The paper presents, among others, the golden number $\varphi $ as the limit of the quotient of neighboring terms of the Fibonacci and Fibonacci type sequence by means of a fixed point of a mapping of a certain interval with the help of Edelstein’s theorem. To demonstrate the equality  , where $f_n$ is $n$-th Fibonacci number also the formula from Corollary has been applied. It was obtained using some relationships between Fibonacci and Lucas numbers, which were previously justified.},
author = {Eugeniusz Barcz},
journal = {Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia},
language = {eng},
pages = {25-35},
title = {On the golden number and Fibonacci type sequences},
url = {http://eudml.org/doc/296320},
volume = {11},
year = {2019},
}

TY - JOUR
AU - Eugeniusz Barcz
TI - On the golden number and Fibonacci type sequences
JO - Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
PY - 2019
VL - 11
SP - 25
EP - 35
AB - The paper presents, among others, the golden number $\varphi $ as the limit of the quotient of neighboring terms of the Fibonacci and Fibonacci type sequence by means of a fixed point of a mapping of a certain interval with the help of Edelstein’s theorem. To demonstrate the equality  , where $f_n$ is $n$-th Fibonacci number also the formula from Corollary has been applied. It was obtained using some relationships between Fibonacci and Lucas numbers, which were previously justified.
LA - eng
UR - http://eudml.org/doc/296320
ER -