Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia, Tome 11 (2019) no. 1, pp. 25-35
Citer cet article
Barcz, Eugeniusz. On the golden number and Fibonacci type sequences. Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia, Tome 11 (2019) no. 1, pp. 25-35. http://geodesic.mathdoc.fr/item/AUPCDM_2019_11_1_a1/
@article{AUPCDM_2019_11_1_a1,
author = {Barcz, Eugeniusz},
title = {On the golden number and {Fibonacci} type sequences},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia},
pages = {25--35},
year = {2019},
volume = {11},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/AUPCDM_2019_11_1_a1/}
}
TY - JOUR
AU - Barcz, Eugeniusz
TI - On the golden number and Fibonacci type sequences
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
PY - 2019
SP - 25
EP - 35
VL - 11
IS - 1
UR - http://geodesic.mathdoc.fr/item/AUPCDM_2019_11_1_a1/
LA - en
ID - AUPCDM_2019_11_1_a1
ER -
%0 Journal Article
%A Barcz, Eugeniusz
%T On the golden number and Fibonacci type sequences
%J Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
%D 2019
%P 25-35
%V 11
%N 1
%U http://geodesic.mathdoc.fr/item/AUPCDM_2019_11_1_a1/
%G en
%F AUPCDM_2019_11_1_a1
The paper presents, among others, the golden number φ 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.
