Diophantine approximation
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.
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1955 in scienceAleksandr KhinchinAlexander OppenheimAlfred van der PoortenAlgebraic number theoryAlmost periodic functionAnalytic number theoryAnatole KatokApproximationArithmetic of abelian varietiesAxel ThueBadly approximable numberBlichfeldt's theoremBrjuno numberCarl D. OldsCarl Ludwig SiegelCarl StørmerChampernowne constantClaude ChabautyContinued fractionDavenport–Schmidt theoremDavid MasserDenjoy's theorem on rotation numberDense setDiophantineDiophantine ApproximationDiophantine approximationsDiophantine equationDiophantusDirichlet's approximation theoremDiscrete mathematicsDonald C. SpencerDuffin–Schaeffer conjectureEquidistributed sequenceEquidistribution theoremErgodic theoryEuclidean algorithmExceptional objectExponential sumFaltings's theorem
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Diophantine approximation
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.
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Aproksymacja diofantyczna – dz ...... najbliższej liczby całkowitej:
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En teoría de números, las apro ...... se aproximan a un número real.
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En théorie des nombres, l'appr ...... de la taille du dénominateur.
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In de getaltheorie, een deelge ...... stelling van Thue-Siegel-Roth.
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In number theory, the study of ...... tudy of Diophantine equations.
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Inom matematiken är Diofantisk ...... ien av Diofantiska ekvationer.
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L'approssimazione diofantea è ...... greco Diofanto di Alessandria.
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Na teoria dos números, a aprox ...... ela desvantagem de aplicações.
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Диофантово приближение имеет д ...... зучении диофантовых уравнений.
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Діофантова апроксімація або Ді ...... теорія трансцендентних чисел.
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Axel Thue
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Carl Ludwig Siegel
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Freeman Dyson
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Klaus Roth
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first
Axel
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Freeman
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Klaus
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frst
Carl Ludwig
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id
p/d032600
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last
Dyson
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Roth
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Siegel
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Thue
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title
Diophantine approximations
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Aproksymacja diofantyczna – dz ...... nie nie da się już zmniejszyć.
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En teoría de números, las apro ...... njunto de los números reales).
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En théorie des nombres, l'appr ...... précision de l'approximation.
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In de getaltheorie, een deelge ...... "kwaliteit" van de benadering.
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In number theory, the study of ...... means of continued fractions.
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Inom matematiken är Diofantisk ...... -talet med hjälp av kedjebråk.
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L'approssimazione diofantea è ...... greco Diofanto di Alessandria.
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Na teoria dos números, a aprox ...... ção do tamanho do denominador.
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Диофантово приближение имеет д ...... осредством непрерывных дробей.
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Діофантова апроксімація або Ді ...... теорія трансцендентних чисел.
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label
Approssimazione diofantea
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Approximation diophantienne
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Aproksymacja diofantyczna
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Aproximación diofántica
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Aproximação diofantina
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Diofantische benadering
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Diofantisk approximation
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Diophantine approximation
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Diophantische Approximation
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Диофантово приближение
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