Concept information
Preferred term
Diophantine approximation
Definition(s)
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In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number a/b is a "good" approximation of a real number α if the absolute value of the difference between a/b and α may not decrease if a/b is replaced by another rational number with a smaller denominator. This problem was solved during the 18th century by means of continued fractions.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Diophantine_approximation)
Broader concept(s)
Narrower concept(s)
- Baker's theorem
- decimal representation
- Dirichlet's theorem on Diophantine approximation
- Duffin-Schaeffer theorem
- equidistributed sequence
- Gelfond-Schneider theorem
- geometry of numbers
- Hurwitz's theorem
- Kronecker's theorem
- Liouville number
- Liouville's theorem on Diophantine approximation
- Littlewood conjecture
- lonely runner conjecture
- normal number
- Oppenheim conjecture
- Roth's theorem
- Siegel's lemma
- Stoneham number
- subspace theorem
- Thue's lemma
In other languages
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French
URI
http://data.loterre.fr/ark:/67375/PSR-Z1B19BG4-0
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