# On the golden number and Fibonacci type sequences

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia (2019)

- Volume: 11, page 25-35
- ISSN: 2080-9751

## Access Full Article

top## Abstract

top## How to cite

topEugeniusz 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.