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This book covers new ground on Fibonacci sequences and the well-known Fibonacci numbers. It will appeal to research mathematicians wishing to advance the new ideas themselves, and to recreational mathematicians, who will enjoy the various visual approaches and the problems inherent in them.There is a continuing emphasis on diagrams, both geometric and combinatorial, which helps to tie disparate topics together, weaving around the unifying themes of the golden mean and various generalizations of the Fibonacci recurrence relation.Very little prior mathematical knowledge is assumed, other than the rudiments of algebra and geometry, so the book may be used as a source of enrichment material and project work for college students. A chapter on games using goldpoint tiles is included at the end, and it can provide much material for stimulating mathematical activities involving geometric puzzles of a combinatoric nature.

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CHOICE Review

Quite the special topic, the Fibonacci numbers nevertheless enjoy enormous popularity, perhaps due to their connection with the golden mean. Vorobiev's book, now translated, presents a solid overview, perfectly pitched to undergraduates. The present version evolved out of a pamphlet written in the 1950s for high school students, but the book now speaks to a more sophisticated audience and reflects the new developments of the intervening years, especially the beautiful role of Fibonacci numbers in Matiyasevich's groundbreaking negative solution of Hilbert's tenth problem. The last chapter develops an unusual computer science application of Fibonacci numbers, a search algorithm developed by J. Kiefer. Despite its title, New Visual Perspectives on Fibonacci Numbers says little about the Fibonacci numbers per se. Rather, Atanassov and colleagues discuss various analogs of the Fibonacci recurrence operating not on numbers, but on other structures: vectors, trees, matrices. The book appears to consolidate years of investigations by a small coterie writing for one another. Their desultory steps do not quite amount to a solid narrative. Even so, creative undergraduates might spin a research project out of this or that intermediate result. Not an urgent acquisition though. ^BSumming Up: Vorobiev--recommended; upper-division undergraduates and up. Atanassov et al.--optional; upper-division undergraduates and up. D. V. Feldman University of New Hampshire