THE GOLDEN RATIO FAMILY AND GENERALIZED FIBONACCI NUMBERS

Anthony G. Shannona; J.V. Leyendekkers

doi:10.24297/jam.v10i1.1401

THE GOLDEN RATIO FAMILY AND GENERALIZED FIBONACCI NUMBERS

Authors

Anthony G. Shannona Faculty of Engineering & IT, University of Technology, Sydney, NSW 2007,
J.V. Leyendekkers aFaculty of Science, The University of Sydney, NSW 2006, Australia

DOI:

https://doi.org/10.24297/jam.v10i1.1401

Keywords:

Modular rings, golden ratio, infinite series, floor function, ceiling function, Fibonacci sequence, divisor function.

Abstract

The equation is used for a golden ratio family to calculate for a range of values of a in the modular ring Z₄. The decimal part of j_a is then used for x in the infinite series for which the associated sums are found. These lead to a series of generalized Fibonacci sequences.

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Published

2015-02-16

How to Cite

Shannona, A. G., & Leyendekkers, J. (2015). THE GOLDEN RATIO FAMILY AND GENERALIZED FIBONACCI NUMBERS. JOURNAL OF ADVANCES IN MATHEMATICS, 10(1), 3130–3137. https://doi.org/10.24297/jam.v10i1.1401