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10 - Continued Fractions

Table of contents

  • 10.1 Finite Continued Fractions
  • 10.2 Convergents to a Continued Fraction
  • 10.3 Continued Fractions with Positive Quotients
  • 10.4 Simple Continued Fractions
  • 10.5 The Representation of an Irreducible Rational Fraction by a Simple Continued Fraction
  • 10.6 The Continued Fraction Algorithm and Euclid’s Algorithm
  • 10.7 The Difference Between the Fraction and its Convergents
  • 10.8 Infinite Simple Continued Fractions
  • 10.9 The Representation of an Irrational Number by an Infinite Continued Fraction
  • 10.10 A Lemma
  • 10.11 Equivalent Numbers
  • 10.12 Periodic Continued Fractions
  • 10.13 Some Special Quadratic Surds
  • 10.14 The Series of Fibonacci and Lucas
  • 10.15 Approximation by Convergents

10.1 Finite Continued Fractions

10.2 Convergents to a Continued Fraction

10.3 Continued Fractions with Positive Quotients

10.4 Simple Continued Fractions

10.5 The Representation of an Irreducible Rational Fraction by a Simple Continued Fraction

10.6 The Continued Fraction Algorithm and Euclid’s Algorithm

10.7 The Difference Between the Fraction and its Convergents

10.8 Infinite Simple Continued Fractions

10.9 The Representation of an Irrational Number by an Infinite Continued Fraction

10.10 A Lemma

10.11 Equivalent Numbers

10.12 Periodic Continued Fractions

10.13 Some Special Quadratic Surds

10.14 The Series of Fibonacci and Lucas

10.15 Approximation by Convergents


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