Golden Ratio And Fibonacci Numbers, The
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A01=Richard A Dunlap
Aperiodicity
Author_Richard A Dunlap
Category=PBH
Category=PBW
Continued Fractions
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Fibonacci Numbers
Geometry
Golden Ratio
Incommensurate Structures
Lucas Numbers
Number Theory
Numerical Sequences
Optimization Algorithms
Quasicrystallography
Tilings
Product details
- ISBN 9789810232641
- Publication Date: 17 Dec 1997
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
