Geodesic
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 Cet article a éte moissonné depuis la source The Polish Digital Mathematics Library

Voir la notice de l'article

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. 
@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
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/