GOLDEN RATIO AND FIBONACCI NUMBERS, THE

GOLDEN RATIO AND FIBONACCI NUMBERS, THE

<p><em>"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."</em></p><p><em>The Fibonacci Quarterly</em></p><p> </p><p>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.</p>