An Introduction to Diophantine Approximation
E654582
"An Introduction to Diophantine Approximation" is a classic mathematical monograph that systematically develops the theory of approximating real numbers by rationals, aimed at advanced undergraduates and researchers in number theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| An Introduction to Diophantine Approximation canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7304622 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: An Introduction to Diophantine Approximation Context triple: [J. W. S. Cassels, notableWork, An Introduction to Diophantine Approximation]
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A.
Diophantine approximation
Diophantine approximation is a branch of number theory that studies how closely real numbers can be approximated by rational numbers, often with quantitative bounds on the quality of approximation.
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B.
Baker theorem on linear forms in logarithms
The Baker theorem on linear forms in logarithms is a fundamental result in transcendental number theory that provides explicit lower bounds for nonzero linear combinations of logarithms of algebraic numbers, with powerful applications to Diophantine equations and Diophantine approximation.
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C.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
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D.
Dirichlet approximation theorem
The Dirichlet approximation theorem is a fundamental result in Diophantine approximation that guarantees, for any real number and positive integer, the existence of a nearby rational number with bounded denominator and small approximation error.
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E.
Three Pearls of Number Theory
Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: An Introduction to Diophantine Approximation Target entity description: "An Introduction to Diophantine Approximation" is a classic mathematical monograph that systematically develops the theory of approximating real numbers by rationals, aimed at advanced undergraduates and researchers in number theory.
-
A.
Diophantine approximation
Diophantine approximation is a branch of number theory that studies how closely real numbers can be approximated by rational numbers, often with quantitative bounds on the quality of approximation.
-
B.
Baker theorem on linear forms in logarithms
The Baker theorem on linear forms in logarithms is a fundamental result in transcendental number theory that provides explicit lower bounds for nonzero linear combinations of logarithms of algebraic numbers, with powerful applications to Diophantine equations and Diophantine approximation.
-
C.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
-
D.
Dirichlet approximation theorem
The Dirichlet approximation theorem is a fundamental result in Diophantine approximation that guarantees, for any real number and positive integer, the existence of a nearby rational number with bounded denominator and small approximation error.
-
E.
Three Pearls of Number Theory
Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
- F. None of above. chosen
Statements (24)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ |
| academicDiscipline | pure mathematics ⓘ |
| describedAs | classic text in Diophantine approximation ⓘ |
| educationalLevel |
graduate
ⓘ
upper undergraduate ⓘ |
| field |
Diophantine approximation
NERFINISHED
ⓘ
number theory ⓘ |
| genre |
mathematics textbook
ⓘ
research monograph ⓘ |
| hasFormat |
book
ⓘ
print ⓘ |
| intendedAudience |
advanced undergraduates
ⓘ
researchers in number theory ⓘ |
| language | English ⓘ |
| mainSubject | approximation of real numbers by rational numbers ⓘ |
| purpose |
introduction to rational approximation methods
ⓘ
systematic development of Diophantine approximation theory ⓘ |
| topic |
Diophantine equations
NERFINISHED
ⓘ
Diophantine inequalities ⓘ continued fractions ⓘ metric Diophantine approximation NERFINISHED ⓘ rational approximation of irrationals ⓘ uniform approximation ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: An Introduction to Diophantine Approximation Description of subject: "An Introduction to Diophantine Approximation" is a classic mathematical monograph that systematically develops the theory of approximating real numbers by rationals, aimed at advanced undergraduates and researchers in number theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.