The Golden Ratio and Fibonacci Numbers
By:Richard A Dunlap
Published on 1997-12-16 by World Scientific
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. Contents:Basic Properties of the Golden RatioGeometric Problems in Two DimensionsGeometric Problems in Three DimensionsFibonacci NumbersLucas Numbers and Generalized Fibonacci NumbersContinued Fractions and Rational ApproximantsGeneralized Fibonacci Representation TheoremsOptimal Spacing and Search AlgorithmsCommensurate and Incommensurate ProjectionsPenrose TilingsQuasicrystallographyBiological ApplicationsConstruction of the Regular PentagonThe First 100 Fibonacci and Lucas NumbersRelationships Involving the Golden Ratio and Generalized Fibonacci Numbers Readership: Applied mathematicians. keywords:Golden Ratio;Fibonacci Numbers;Number Theory;Quasicrystallography;Tilings;Geometry;Optimization Algorithms;Numerical Sequences;Lucas Numbers;Continued Fractions;Aperiodicity;Incommensurate Structures |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
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Book ID of The Golden Ratio and Fibonacci Numbers's Books is qBftCgAAQBAJ, Book which was written byRichard A Dunlaphave ETAG "8zjSU2JehRU"
Book which was published by World Scientific since 1997-12-16 have ISBNs, ISBN 13 Code is 9789814496940 and ISBN 10 Code is 9814496944
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