Generalized metallic means

Juan Bautista Gil, Aaron Worley

Research output: Contribution to journalArticle

Abstract

The metallic means (also known as metallic ratios) may be defined as the limiting ratio of consecutives terms of sequences connected to the Fibonacci sequence via the invert transform. For example, the Pell sequence (invert transform of the Fibonacci sequence) gives the so-called silver mean, and the invert transform of the Pell sequence leads to the bronze mean. The limiting ratio of the Fibonacci sequence itself is known as the golden mean or ratio. We introduce a new family of kth degree metallic means obtained through invert transforms of the generalized kth order Fibonacci sequence. As in the case k = 2, each generalized metallic mean is shown to be the unique positive root of a kth degree polynomial determined by the sequence.

Original languageEnglish (US)
Pages (from-to)45-50
Number of pages6
JournalFibonacci Quarterly
Volume57
Issue number1
StatePublished - Feb 1 2019

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Fibonacci sequence
Invert
Transform
Limiting
Order of a polynomial
Silver
Consecutive
Roots
Term

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Gil, J. B., & Worley, A. (2019). Generalized metallic means. Fibonacci Quarterly, 57(1), 45-50.
Gil, Juan Bautista ; Worley, Aaron. / Generalized metallic means. In: Fibonacci Quarterly. 2019 ; Vol. 57, No. 1. pp. 45-50.
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Gil, JB & Worley, A 2019, 'Generalized metallic means', Fibonacci Quarterly, vol. 57, no. 1, pp. 45-50.

Generalized metallic means. / Gil, Juan Bautista; Worley, Aaron.

In: Fibonacci Quarterly, Vol. 57, No. 1, 01.02.2019, p. 45-50.

Research output: Contribution to journalArticle

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Gil JB, Worley A. Generalized metallic means. Fibonacci Quarterly. 2019 Feb 1;57(1):45-50.