On the golden number and Fibonacci type sequences

• Autorzy: Eugeniusz Barcz

Warianty tytułu

PL

On the golden number and Fibonacci type sequences

• Języki publikacji: EN

Abstrakty

EN

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 \ref{cor1} has been applied. It was obtained using some relationships between Fibonacci and Lucas numbers, which were previously justified.

• Wydawca: Wydawnictwo Naukowe Uniwersytetu Pedagogicznego
• Czasopismo: Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
• Rocznik: 2019
• Tom: 11
• Strony: 25-35

Daty

wydano

2020-02-05

Twórcy

autor

Eugeniusz Barcz

Identyfikatory

DOI

10.24917/20809751.11.2