Lagrange Number (Rational Approximation)
Hurwitz's Irrational Number Theorem gives the best rational approximation possible for an arbitrary irrationalnumber 
as
The
are called Lagrange numbers and get steadily larger for each ``bad'' set of irrational numbers which is excluded. | Exclude | |
| 1 | none |  |
| 2 |  |  |
| 3 |  |  |
Lagrange numbers are of the form
where
is a Markov Number. The Lagrange numbers form a Spectrum called theLagrange Spectrum.See also Hurwitz's Irrational Number Theorem, Liouville's Rational Approximation Theorem, Liouville-RothConstant, Markov Number, Roth's Theorem, Spectrum Sequence, Thue-Siegel-Roth Theorem
References
Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 187-189, 1996.
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