Back Satz von Thue-Siegel-Roth German Teorema de Roth Spanish Théorème de Roth French Thue–Siegel–Roth-tétel Hungarian トゥエ・ジーゲル・ロスの定理 Japanese Stelling van Thue-Siegel-Roth Dutch Twierdzenie Thue-Siegela-Rotha Polish Теорема Туэ — Зигеля — Рота Russian
In mathematics, Roth's theorem or Thue–Siegel–Roth theorem is a fundamental result in diophantine approximation to algebraic numbers. It is of a qualitative type, stating that algebraic numbers cannot have many rational approximations that are 'very good'. Over half a century, the meaning of very good here was refined by a number of mathematicians, starting with Joseph Liouville in 1844 and continuing with work of Axel Thue (1909), Carl Ludwig Siegel (1921), Freeman Dyson (1947), and Klaus Roth (1955).