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2009•International journal of mathematics and computationRequires access

Infinite Family of Generalized Golden Ratios

Mohammed Yahdi

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Abstract

The paper explores the generalization of the Fibonacci Golden Ratio to an infinite sequence of k-Golden Ratios. An extension of Binet’s Formula generates an infinite family of Fibonacci-like sequences. Each of these sequences is shown to possess the property that the quotient of consecutive terms converges to the corresponding k-Golden Ratio.

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What this paper is about

The paper explores the generalization of the Fibonacci Golden Ratio to an infinite sequence of k-Golden Ratios. An extension of Binet’s Formula generates an infinite family of Fibonacci-like sequences. Each of these sequences is shown to possess the property that the quotient of consecutive terms converges to the corresponding k-Golden Ratio.

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Available abstract

The paper explores the generalization of the Fibonacci Golden Ratio to an infinite sequence of k-Golden Ratios. An extension of Binet’s Formula generates an infinite family of Fibonacci-like sequences. Each of these sequences is shown to possess the property that the quotient of consecutive terms converges to the corresponding k-Golden Ratio.

Key concepts: Golden ratio, Fibonacci number, Mathematics, Generalization, Quotient, Combinatorics, Property (philosophy), Sequence (biology)

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