Phidias numbers as a basis for Fibonacci analogues

P. S. Kosobutskyy
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 1, Pages 172-178
DOI: 10.7546/nntdm.2020.26.1.172-178
Full paper (PDF, 452 Kb)

Details

Authors and affiliations

P. S. Kosobutskyy
Department of Computer-Aided Design
Lviv Polytechnic National University
S. Bandery 12 St., Lviv, 79646, Ukraine

Abstract

In this paper it is shown that there is a plurality of irrational values of the roots of a quadratic equation with equal modulus coefficients |p| = |q| ≠ 1 having properties of the numbers of Phidias φ = 0.61803… and Ф = 1.61803… It is shown that it is also possible to construct a set of sequences possessing the basic properties of the Fibonacci and Lucas sequences.

Keywords

• Golden ratio
• Quadratic irrationality
• Roots of quadratic equation

2010 Mathematics Subject Classification

• 11B37
• 11B39

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