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- Lochs'_theorem abstract "In number theory, Lochs' theorem is a theorem concerning the rate of convergence of the continued fraction expansion of a typical real number. A proof of the theorem was published by Gustav Lochs in 1964.The theorem states that for almost all real numbers in the interval (0,1), the number of terms m of the number's continued fraction expansion that are required to determine the first n places of the number's decimal expansion behaves asymptotically as follows:(sequence A086819 in OEIS).As this limit is only slightly smaller than 1, this can be interpreted as saying that each additional term in the continued fraction representation of a "typical" real number increases the accuracy of the representation by approximately one decimal place. The decimal system is the last positional system for which each digit carries less information than one continued fraction quotient; going to base-11 (changing to in the equation) makes the above value exceed 1.The reciprocal of this limit,(sequence A062542 in OEIS),is twice the base-10 logarithm of Lévy's constant.".
- Lochs'_theorem wikiPageID "18266692".
- Lochs'_theorem wikiPageRevisionID "543402612".
- Lochs'_theorem hasPhotoCollection Lochs'_theorem.
- Lochs'_theorem subject Category:Continued_fractions.
- Lochs'_theorem subject Category:Theorems_in_number_theory.
- Lochs'_theorem type Abstraction100002137.
- Lochs'_theorem type Communication100033020.
- Lochs'_theorem type ComplexNumber113729428.
- Lochs'_theorem type ContinuedFraction113736550.
- Lochs'_theorem type ContinuedFractions.
- Lochs'_theorem type DefiniteQuantity113576101.
- Lochs'_theorem type Fraction113732078.
- Lochs'_theorem type Measure100033615.
- Lochs'_theorem type Message106598915.
- Lochs'_theorem type Number113582013.
- Lochs'_theorem type Proposition106750804.
- Lochs'_theorem type RationalNumber113730469.
- Lochs'_theorem type RealNumber113729902.
- Lochs'_theorem type Statement106722453.
- Lochs'_theorem type Theorem106752293.
- Lochs'_theorem type TheoremsInNumberTheory.
- Lochs'_theorem comment "In number theory, Lochs' theorem is a theorem concerning the rate of convergence of the continued fraction expansion of a typical real number.".
- Lochs'_theorem label "Lochs' theorem".
- Lochs'_theorem label "Satz von Lochs".
- Lochs'_theorem label "Teorema de Lochs".
- Lochs'_theorem label "Théorème de Lochs".
- Lochs'_theorem sameAs Satz_von_Lochs.
- Lochs'_theorem sameAs Teorema_de_Lochs.
- Lochs'_theorem sameAs Théorème_de_Lochs.
- Lochs'_theorem sameAs m.04cy63n.
- Lochs'_theorem sameAs Q1576235.
- Lochs'_theorem sameAs Q1576235.
- Lochs'_theorem sameAs Lochs'_theorem.
- Lochs'_theorem wasDerivedFrom Lochs'_theorem?oldid=543402612.
- Lochs'_theorem isPrimaryTopicOf Lochs'_theorem.