2015JOURNAL OF ADVANCES IN MATHEMATICSOpen access

THE GOLDEN RATIO FAMILY AND GENERALIZED FIBONACCI NUMBERS

Anthony G. Shannona, J. V. Leyendekkers

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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 ja 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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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 ja 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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Available 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 ja 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.

Key concepts: Fibonacci number, Mathematics, Golden ratio, Decimal, Ring (chemistry), Series (stratigraphy), Arithmetic, Range (aeronautics)

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