Continued fractions

Front Cover
 Continued Fractions
 Copyright Page
 Contents
 Preface
 Chapter 1. Expansion of Rational Fractions
 1.1 Introduction
 1.2 Definitions and Notation
 1.3 Expansion of Rational Fractions
 1.4 Expansion of Rational Fractions (General Discussion)
 1.5 Convergents and Their Properties
 1.6 Differences of Convergents
 1.7 Some Historical Comments
 Chapter 2. Diophantine Equations
 2.1 Introduction
 2.2 The Method Used Extensively by Euler
 2.3 The Indeterminate Equation ax --
by = 1
 2.4 The General Solution of ax --
by = c, (a, b) = 1
 2.5 The General Solution of ax + by = c, (a, b) = 1. 2.6 The General Solution of Ax By = C2.7 Sailors, Coconuts, and Monkeys
 Chapter 3. Expansion of Irrational Numbers
 3.1 Introduction
 3.2 Preliminary Examples
 3.3 Convergents
 3.4 Additional Theorems on Convergents
 3.5 Some Notions of a Limit
 3.6 Infinite Continued Fractions
 3.7 Approximation Theorems
 3.8 Geometrical Interpretation of Continued Fractions
 3.9 Solution of the Equation x2 = ax + 1
 3.10 Fibonacci Numbers
 3.11 A Method for Calculating Logarithms
 Chapter 4. Periodic Continued Fractions
 4.1 Introduction
 4.2 Purely Periodic Continued Fractions. 4.3 Quadratic Irrationals4.4 Reduced Quadratic Irrationals
 4.5 Converse of Theorem 4.1
 4.6 Lagrange's Theorem
 4.7 The Continued Fraction for N
 4.8 Pell's Equation, x2 --
Ny2 = 1
 4.9 How to Obtain Other Solutions of Pell's Equation
 Chapter 5. Epilogue
 5.1 Introduction
 5.2 Statement of the Problem
 5.3 Hurwitz' Theorem
 5.4 Conclusion
 Appendix I. Proof That x2 --
3y2 = --
1 Has No Integral Solutions
 Appendix II. Some Miscellaneous Expansions
 Solutions to Problems
 References
 Index.