Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications

Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications

by Steven Vajda

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Overview


This text for advanced undergraduates and graduate students surveys the use of Fibonacci and Lucas numbers in areas relevant to operational research, statistics, and computational mathematics. It also covers geometric topics related to the ancient principle known as the Golden Section—a mystical expression of aesthetic harmony that bears a close connection with the Fibonacci mechanism.
The Fibonacci principle of forming a new number by an appropriate combination of previous numbers has been extended to yield sequences with surprising and sometimes mystifying properties: the Meta-Fibonacci sequences. This text examines Meta-Fibonacci numbers, proceeding to a survey of the Golden Section in the plane and space. It also describes Platonic solids and some of their less familiar features, and an appendix and other supplements offer helpful background information. Students and teachers will find this book relevant to studies of algebra, geometry, probability theory, computational aspects, and combinatorial aspects of number theory.
Steven Vajda was born in Budapest in 1901 and died in England in 1995. For the last twenty-two years of his life, he was Visiting Professor of Mathematics at Sussex University. As a prominent teacher, lecturer, and author he played a vital role in the development of mathematical programming and operations research and wrote more than a dozen books and many research papers on these and other topics including game theory.

Product Details

ISBN-13: 9780486462769
Publisher: Dover Publications
Publication date: 12/26/2007
Series: Dover Books on Mathematics Series
Pages: 192
Product dimensions: 6.14(w) x 9.21(h) x (d)

About the Author



Steven Vajda (1901–95) was Visiting Professor of Mathematics at England's Sussex University.

Table of Contents


Preface
Introduction
Background
Relationships
Fibonacci numbers and the Golden Section
Fibonacci Series
Divisibility properties
Congruences and uniformity
Continued fractions and convergents
Fibonacci representation
Search and games
Hyperbolic functions and Fibonacci numbers
Meta-Fibonacci sequences (a letter from B. W. Conolly)
The Golden Section in the plane
The Golden Section in three-dimensional space
Appendix
List of formulae
References
Table of Fn and Ln and their prime factors
Index

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