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The Golden Ratio & Fibonacci Numbers

by Dunlap R a

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Patterns linking number theory, geometry, and nature

$65.65 USD
$72.95 USD $65.65 USD
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Hardcover New English

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Awards & Recognition

  • Critical praise

    Praised by The Fibonacci Quarterly

    The journal praises the book as attractive, carefully written, and a valuable addition to academic and personal ...

AlbakiReads Editorial

Patterns linking number theory, geometry, and nature

Dunlap’s book develops the mathematical properties of the golden ratio alongside the Fibonacci and generalized Fibonacci sequences. It connects these ideas to figures with fivefold symmetry, then extends the discussion into practical algorithms for searching and function minimization. The scope also reaches aperiodic structures: Fibonacci sequences are considered as one-dimensional aperiodic lattices, with related concepts carried into Penrose tilings, incommensurate projections, and the structure of aperiodic crystals. Biological growth provides another application, giving the book a bridge between abstract mathematical patterns and physical or living forms.

Good fit for readers who enjoy

  • General readers with an interest in mathematics and its applications to physical or biological sciences
  • Readers exploring number theory, Fibonacci sequences, or the golden ratio
  • Those interested in mathematical connections to algorithms, tilings, crystals, and biological growth

Themes

Golden ratio and Fibonacci sequencesFivefold symmetry and geometrySearch and function-minimization algorithmsAperiodic lattices, Penrose tilings, and crystalsMathematical patterns in biological growth

Based on publisher information and book metadata.

Book overview

"This attractive and carefully written book addresses the general reader with interest in mathematics and its application to the physical and biological sciences ... this one will make a valuable addition to academic and personal libraries."

The Fibonacci Quarterly

 

In this invaluable book, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Fibonacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms for searching and function minimization. The Fibonacci sequence is viewed as a one-dimensional aperiodic, lattice and these ideas are extended to two- and three-dimensional Penrose tilings and the concept of incommensurate projections. The structural properties of aperiodic crystals and the growth of certain biological organisms are described in terms of Fibonacci sequences.

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