KnowraDiophantine approximationLinked fromLinked fromThe 14 pages that link to Diophantine approximation, each with the reason it gives.All 14Related 6Narrower topic 8Irrational numberRelated: Irrational numbers can be approached by fractions, though never represented exactly by one.Continued fractionNarrower topic: Continued fractions provide systematic solutions to rational-approximation problems.Transcendental numberRelated: Approximation quality supplies both criteria for transcendence and measures of its strength.Geometry of numbersRelated: Minkowski's geometric methods supplied powerful results about rational approximations.Joseph LiouvilleNarrower topic: Liouville’s theorem is an early landmark in this broader subject.Dirichlet's approximation theoremNarrower topic: Dirichlet's theorem is a foundational universal result in this broader area.Egyptian fractionRelated: Egyptian fractions provide constrained rational representations that connect to approximation questions.Transcendence theoryRelated: Approximation bounds are a major route to proving transcendence.Siegel's lemmaNarrower topic: The lemma belongs to a tradition of deriving small integer relations through approximation.Apéry's theoremNarrower topic: The proof constrains rational approximations to ζ(3) until irrationality follows.Lochs's theoremNarrower topic: Continued-fraction prefixes encode strong rational approximations, linking the theorem to approximation precision.Lonely runner conjectureRelated: Relative runner positions encode simultaneous approximation conditions.Thue's lemmaNarrower topic: Thue's lemma supplies small integer vectors used to derive rational approximations.Tijdeman's theoremNarrower topic: The proof's quantitative control of logarithmic expressions belongs to a broader approximation tradition.