Fibonacci numbers

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). The prerequisites for reading this book are minimal. A certain acquaintance with elementary operations and a readyness for mathematical thought are enough to follow the presentation to remarkable mathematical depths. Apart from anybody interested in the Fibonacci numbers as such, the book can be used for under-graduate courses on this subject, touching on several mathematical areas on the way. Fibonacci numbers create a fascinating and beautiful world of original problems which many amateurs and professionals find exciting to explore. The books is an invitation and a comprehensive guidebook to this world.