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.

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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. 
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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/