Algebraic numbers 45
Algebraic numbers of degree n 45 50
Algebraic numbers, quadratic 45 47-50 62
Almost all 62
Approximant see "Convergents"
Arithmetic mean of the first n elements of a continued fraction 93
Best approximations 20 21-22
Best approximations of the first kind 24
Best approximations of the second kind 24
Bounded elements, irrational numbers with 36 60-62
Canonical representation of a finite continued fraction 3
Canonical representation of a segment 4
Chebyshev, P.L. 38 39
Convergence of a continued fraction 8
Convergence of a continued fraction, criterion for 10-12
Convergents 4 6 30
Convergents as best approximations 20-28
Convergents of a real number 9
Convergents, irreducibility of 12
Convergents, rate of increase of denominators 13 65-66
Convergents, recursion formula for 5
Convergents, rule of formation 4
Density of a number in the first n elements of a continued fraction 92
Density of a number in the sequence of elements of a continued fraction 92-93
Diophantine approximations 38-44
Elements as a function of the number represented 52-60
Elements of a continued fraction 1
Elements of a real number 9
| Finite continued fraction 1
Gauss, K.F. 71 81-86
Geometric mean of the first n elements of a continued fraction 93
Huygens, C. 28
Infinite continued fraction 1
Intermediate continued fractions 13-15
Intermediate continued fractions as best approximations 22
Kuz'min, R.O. 71-82
Lagrange, J.L. 47
Levy, P. 66 71 82
Liouville, J. 45 46 50
Measure of sets 51
Mediant of two fractions 14
Order of a continued fraction 1 2
Order of approximation 28-34 35 62
Ostrogradskii, M.V. 21
Periodic continued fraction 47-50
Rank of an interval 54-57
Regular continued fraction 1
Remainder of a continued fraction 2 8
Remainder of a real number 9
Segment of a continued fraction 2
Segment of a real number 9
Simple continued fraction 1
Systematic fractions 19
Transcendental numbers 45
Transcendental numbers, existence of 47
Uniqueness of representation of numbers 12 16-18
Value of a continued fraction 8 9 12 14
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