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 S3.png is used for a golden ratio family to calculate S5.png for a range of values of a in the modular ring Z4.  The decimal part of ja is then used for x in the infinite seriesS4.png for which the associated sums are found. These lead to  a series of generalized Fibonacci sequences.

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JOURNAL OF ADVANCES IN MATHEMATICS

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Published

2015-02-16

Issue

Vol. 10 No. 1 (2015)

Section

Articles

License

Creative Commons License All articles published in Journal of Advances in Linguistics are licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

THE GOLDEN RATIO FAMILY AND GENERALIZED FIBONACCI NUMBERS. (2015). JOURNAL OF ADVANCES IN MATHEMATICS, 10(1), 3130-3137. https://doi.org/10.24297/jam.v10i1.1401

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