Some characteristics of the Golden Ratio family

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 22, 2016, Number 3, Pages 84–89
Full paper (PDF, 157 Kb)

Details

Authors and affiliations

J. V. Leyendekkers
Faculty of Science, The University of Sydney, NSW 2006, Australia

A. G. Shannon
Faculty of Engineering & IT, University of Technology, Sydney, NSW 2007, Australia
Campion College, PO Box 3052, Toongabbie East, NSW 2146, Australia

Abstract

Research into properties of generalizations of the Golden Ratio has considered various forms of extreme and mean ratios. This is considered here too within the framework of a family of surds, ½ √(1+a), and generalized Fibonacci numbers, F_n(a), with the ordinary Fibonacci numbers being the particular case when a = 5.

Keywords

• Modular rings
• Golden Ratio
• Infinite series
• Binet formula
• Right-end-digits
• Fibonacci sequence

AMS Classification

• 11B39
• 11B50

References

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