Hurwitz's Irrational Number Theorem gives the best rational approximation possible for an arbitrary irrational
Lagrange numbers are of the form
See also Hurwitz's Irrational Number Theorem, Liouville's Rational Approximation Theorem, Liouville-Roth Constant, Markov Number, Roth's Theorem, Spectrum Sequence, Thue-Siegel-Roth Theorem
Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 187-189, 1996.