Fibonacci Numbers

ISBN-13: 9783764361358 / Angielski / Miękka / 2002 / 178 str.

Nicolai N. Vorobiev;M. Martin

Opis

Since their discovery hundreds of years ago, people have been fascinated by the wondrous properties of Fibonacci numbers. Being of mathematical significance in their own right, Fibonacci numbers have had an impact on areas like art and architecture, and their traces can be found in nature and even the behavior of the stock market. Starting with the basic properties of Fibonacci numbers, the present book explores their relevance in number theory, the theory of continued fractions, geometry and approximation theory. Rather than giving a complete account of the subject, a few chosen examples are treated exhaustively. They not only reveal the bearing of Fibonacci numbers on mathematics, but also provide very readable marvels of mathematical reasoning. This book is the translation of the 6th Russian edition (the first edition appeared in the early fifties and became a standard source of information on the subject).

Recenzje

"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. . . . Recommended; upper-division undergraduates and up."

-CHOICE

"This is a wonderful book with a huge amount of information on Fibonacci numbers. First published in the 1950s for high school students enrolled in a mathematical circle at the Leningrad State University, the book only assumes knowledge of high school mathematics, but the reader will need the sophistication of a good upper-level mathematics major. The warmth and enthusiasm of the late author comes through Mircea Martin's English translation.... This book would be useful to any mathematician with a desire to know more about the Fibonacci numbers. A student could use it for a reading project on the Fibonacci numbers.... Overall, I enjoyed the book and highly recommend it."

-MAA Online

Spis treści

1 The Simplest Properties of Fibonacci Numbers.- 2 Number-Theoretic Properties of Fibonacci Numbers.- 3 Fibonacci Numbers and Continued Fractions.- 4 Fibonacci Numbers and Geometry.- 5 Fibonacci Numbers and Search Theory.