Books  Physical Sciences  Mathematics 

The Golden Ratio and Fibonacci Numbers

By: Richard A Dunlap

162 pages, Illus, figs, tabs

World Scientific Publishing

Hardback | Feb 1998 | #88459 | ISBN: 9810232640
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NHBS Price: £37.99 $46/€43 approx

About this book

In this text, 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 Finobacci 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, latice 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.


Basic properties of the golden ratio; geometric problems in two dimensions; geometric problems in three dimensions; Fibonacci numbers; Lucas numbers and generalized Fibonacci numbers; continued fractions and rational approximants; generalized Fibonacci representation theorems; optimal spacing and search algorithms; commensurate and incommensurate projections; Penrose tilings; quasicrystallography; biological applications; construction of the regular pentagon; the first 100 Fibonacci and Lucas numbers; relationships involving Fibonacci and Lucas numbers.

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