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Tables of Contents for Continued Fractions
Chapter/Section Title
Page #
Page Count
Chapter I. Properties of the Apparatus
1
15
1. Introduction
1
2
2. Convergents
3
5
3. Infinite continued fractions
8
4
4. Continued fractions with natural elements
12
4
Chapter II. The Representation of Numbers by Continued Fractions
16
35
5. Continued fractions as an apparatus for representing real numbers
16
4
6. Convergents as best approximations
20
8
7. The order of approximation
28
6
8. General approximation theorems
34
11
9. The approximation of algebraic irrational numbers and Liouville's transcendental numbers
45
2
10. Quadratic irrational numbers and periodic continued fractions
47
4
Chapter III. The Measure Theory of Continued Fractions
51
44
11. Introduction
51
1
12. The elements as functions of the number represented
52
8
13. Measure-theoretic evaluation of the increase in the elements
60
5
14. Measure-theoretic evaluation of the increase in the denominators of the convergents. The fundamental theorem of the measure theory of approximation
65
6
15. Gauss's problem and Kuz'min's theorem
71
15
16. Average values
86
9
Index
95