**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

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## 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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## Related papers

- Spivey, R. J. (2019). Close encounters of the golden and silver ratios. Notes on Number Theory and Discrete Mathematics, 25(3), 170-184, doi: 10.7546/nntdm.2019.25.3.170-184.

## Cite this paper

APALeyendekkers, J. V., & Shannon, A. G. (2016). Some characteristics of the Golden Ratio family, Notes on Number Theory and Discrete Mathematics, 22(3), 84-89.

ChicagoLeyendekkers, J. V. and A. G. Shannon “Some Characteristics of the Golden Ratio Family.” Notes on Number Theory and Discrete Mathematics 22, no. 3 (2016): 84-89.

MLALeyendekkers, J. V. and A. G. Shannon, “Some Characteristics of the Golden Ratio Family.” Notes on Number Theory and Discrete Mathematics 22.3 (2016): 84-89. Print.