THE GOLDEN RATIO FAMILY AND GENERALIZED FIBONACCI NUMBERS
Anthony G. Shannona, J. V. Leyendekkers
Abstract
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Anthony G. Shannona, J. V. Leyendekkers
Abstract
Open-access reader
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.
Key concepts: Fibonacci number, Mathematics, Golden ratio, Decimal, Ring (chemistry), Series (stratigraphy), Arithmetic, Range (aeronautics)