Continued Fractions /

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Continued fractions were studied by the great mathematicians of the seventeenth and eighteenth centuries and are a subject of active investigation today. Fractions of this form provide much insight into many mathematical problems #x97; particularly into the nature of numbers #x97; and the theory of...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Olds, C. D.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2012.
Colección:Anneli Lax new mathematical library.
Temas:
Continued fractions.
Fractions continues.
MATHEMATICS > Algebra > Intermediate.
Continued fractions
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 â€? by = ±1
  • 2.4 The General Solution of ax
  • by = c, (a, b) = 12.5 The General Solution of ax + by = c, (a, b) = 1
  • 2.6 The General Solution of Ax ± By = ±C
  • 2.7 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 LogarithmsChapter 4. Periodic Continued Fractions
  • 4.1 Introduction
  • 4.2 Purely Periodic Continued Fractions
  • 4.3 Quadratic Irrationals
  • 4.4 Reduced Quadratic Irrationals
  • 4.5 Converse of Theorem 4.1
  • 4.6 Lagrangeâ€?s Theorem
  • 4.7 The Continued Fraction for N
  • 4.8 Pellâ€?s Equation, x2 â€? Ny2 = ±1
  • 4.9 How to Obtain Other Solutions of Pellâ€?s Equation
  • Chapter 5. Epilogue
  • 5.1 Introduction
  • 5.2 Statement of the Problem
  • 5.3 Hurwitzâ€? Theorem
  • 5.4 Conclusion
  • Appendix I. Proof That x2
  • 3y2 = â€? 1 Has No Integral SolutionsAppendix II. Some Miscellaneous Expansions
  • Solutions to Problems
  • References
  • Index

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