Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Diophantine_approximation> ?p ?o. }
Showing items 1 to 34 of
34
with 100 items per page.
- Diophantine_approximation abstract "In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers. 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.Knowing the "best" approximations of a given number, the main problem of the field is to find sharp upper and lower bounds of the above difference, expressed as a function of the denominator.It appears that these bounds depend on the nature of the real numbers to be approximated: the lower bound for the approximation of a rational number by another rational number is larger than the lower bound for algebraic numbers, which is itself larger than the lower bound for all real numbers. Thus a real number that may be better approximated than the bound for algebraic numbers is certainly a transcendental number. This allowed Liouville, in 1844 to produce the first explicit transcendental number. Later, the proofs that π and e are transcendental were obtained with a similar method.Thus Diophantine approximations and transcendence theory are very close areas that share many theorems and methods. Diophantine approximations have also important applications in the study of Diophantine equations.".
- Diophantine_approximation wikiPageExternalLink HCMUNS10.pdf.
- Diophantine_approximation wikiPageID "251558".
- Diophantine_approximation wikiPageRevisionID "606046209".
- Diophantine_approximation hasPhotoCollection Diophantine_approximation.
- Diophantine_approximation id "p/d032600".
- Diophantine_approximation title "Diophantine approximations".
- Diophantine_approximation subject Category:Diophantine_approximation.
- Diophantine_approximation subject Category:Number_theory.
- Diophantine_approximation comment "In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers. 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.".
- Diophantine_approximation label "Approssimazione diofantea".
- Diophantine_approximation label "Approximation diophantienne".
- Diophantine_approximation label "Aproksymacja diofantyczna".
- Diophantine_approximation label "Aproximación diofántica".
- Diophantine_approximation label "Aproximação diofantina".
- Diophantine_approximation label "Diophantine approximation".
- Diophantine_approximation label "Diophantische Approximation".
- Diophantine_approximation label "Diophantische benadering".
- Diophantine_approximation label "Диофантово приближение".
- Diophantine_approximation label "ディオファントス近似".
- Diophantine_approximation label "丟番圖逼近".
- Diophantine_approximation sameAs Diophantische_Approximation.
- Diophantine_approximation sameAs Aproximación_diofántica.
- Diophantine_approximation sameAs Approximation_diophantienne.
- Diophantine_approximation sameAs Approssimazione_diofantea.
- Diophantine_approximation sameAs ディオファントス近似.
- Diophantine_approximation sameAs Diophantische_benadering.
- Diophantine_approximation sameAs Aproksymacja_diofantyczna.
- Diophantine_approximation sameAs Aproximação_diofantina.
- Diophantine_approximation sameAs m.01lbj8.
- Diophantine_approximation sameAs Q1227061.
- Diophantine_approximation sameAs Q1227061.
- Diophantine_approximation wasDerivedFrom Diophantine_approximation?oldid=606046209.
- Diophantine_approximation isPrimaryTopicOf Diophantine_approximation.