Real Numbers and Fascinating Fractions

INDEX

A C E I L M N O P Q R S T U

A
Absolute error
Algebraic equation of degree n
Approximate value
Approximate value by defect
Approximate value in excess
Approximation
Approximation by Convergents
Approximation by defect
Approximation by excess
Approximation of Real Numbers
Arithmetic nature
Average duration of year
Average length of Gregorian year

C
Calendar reform
Calendar problem, use of Continued Fractionsi
Cantor's Continuity Axiom
Charves
Civil year
Classification of Irrationals
Common measure
Comparison of Neighbouring Convergents
Complete quotients
Concept of Convergents
Condition of Rationality of Non-terminating Decimals
Continued fraction
Continued fraction for geometrical quantity
Continuity
Convention of non-terminating decimals
Convergents have the Highest Quality

D
Decimal fraction
Difference Between Two Neighbouring Convergents

E
Ellipsis
End of segment
Error of approximation
Euclid's Algorithm
Evaluation of Convergents
Examples of applications of Euclid's algorithm
Examples of Non-terminating Expansion
Expansion of Negative Numbers into Continued Fractions
Expansion of Ö2 into a continued fraction

H
Half-closed interval
High-quality Approximation
How to Choose a Calendar
How to generate convergents

I
Increment of nth convergent
Infinite
Integral part of continued fraction
Interval
Irrational
Irrational number
Irrational numbers
Irrational Numbers
Irreducibility of convergents

J
Julian calendar
Julius Caesar

L
Leap year

M
Main Property of Convergents
Make-weight
Mathematical Problem of the Calendar
Metius' number
Mixed periodical continued fraction
Mystery of Archimedes' Number

N
Natural numbers
Nature of Numbers Given by Continued Fractions
Non-algebraic numbers
Non-terminating Continued Fractions
Non-terminating decimals
Non-terminating fractions
Normalized error
Notation for Continued Fractions
nth convergent
Numerical Value of a Non-terminating Continued Fraction

O
Open rays
Ordinary year

P
Periodical non-terminating continued fraction
Principle of Nested Segments
Properties of Convergents
Purely periodical continued fraction

Q
Quadratic irrationals
Quadratic Irrationals
Quality factor
Quality of an approximation
Quality of approximation
Rational Numbers, set of

R
Real numbers
Real Numbers
Recursion formula
Representation of Irrationals by Non-terminating Continued Fractions
Representation of Real Numbers on the Number Line

S
Secret of Pope Gregory XIII
Segment
Set of Rational Numbers
Solar day
Solution of the Calendar Problem
Symbol p
Symmetrical correspondence

T
Terminating continued fraction
Terms of continued fraction
Transcendental numbers

U
Upper bound of absolute error

Y
Year