Real Numbers and Fascinating Fractions
INDEX
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
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
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