Fibonacci Numbers

Fibonacci Numbers By Nicolai N. Vorobiev 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.

Introduction:

In elementary mathematics we encounter many challenging and interesting problems, which are not connected with somebody’s name but rather bear the trait of a kind of “mathematical folklore.” Such problems are scattered throughout the existing popular, or purely recreational, mathematical literature and often it is quite difficult to pinpoint the provenience of a specific problem.

These problems frequently circulate in several versions. Sometimes a few such problems come together as a single, more complex, problem; some other times, on the contrary, a single problem is split up into a few simpler problems. In other words, it is seldom possible to figure out where a particular problem ends and another one begins. More to the point, we may think of each such problem as a succinct mathematical theory with its own history, own topics, and own methods, by and large connected with the history, themes, and methods of “great mathematics.”

The theory of Fibonacci numbers is just one of this kind. Originating from the famous Rabbit Problem, and going back in time about 770 years, Fibonacci numbers provide one of the most captivating chapters of elementary mathematics. Problems referring to Fibonacci numbers can be found in many popular publications on mathematics, are studied at meetings of mathematical school societies, and featured in mathematical competitions.

Contents:

• The Simplest Properties of Fibonacci Numbers,
• Number-Theoretic Properties of Fibonacci Numbers
• Fibonacci Numbers and Continued Fractions
• Fibonacci Numbers and Geometry
• Fibonacci Numbers and Search Theory

Fibonacci Numbers By Nicolai N. Vorobiev pdf