KnowraRational approximationLinked fromLinked fromThe 12 pages that link to Rational approximation, each with the reason it gives.All 12Related 4Narrower topic 5Compared with 3Rational numberRelated: Rational numbers can approximate every real number arbitrarily closely.Continued fractionNarrower topic: Continued fractions are a structured method within rational approximation.PiRelated: Fractions such as 22/7 approximate pi but never equal it.Diophantine approximationNarrower topic: Diophantine approximation is the number-theoretic study of rational approximation with explicit error and denominator bounds.Padé approximantNarrower topic: Padé approximants are a systematic local method within this broader subject.Dirichlet's approximation theoremNarrower topic: The theorem gives a universal quantitative guarantee within this broader subject.Hardy–Littlewood circle methodRelated: Dirichlet’s approximation theorem ensures every phase lies near a rational point or in a manageable minor-arc region.Approximation theoryCompared with: Rational functions can represent poles and sharp changes that polynomial approximants handle poorly.Runge's theoremNarrower topic: Runge's theorem gives a foundational existence result for rational approximation in the complex plane.Computable numberRelated: Computability is defined by the ability to produce such approximations on demand.Mergelyan's theoremCompared with: Rational functions can approximate on sets with disconnected complements where polynomials may fail.Proof that π is irrationalCompared with: Excellent rational approximations to π do not make π rational.