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.
General
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