A slightly weaker form of the theorem states that for every real , there exist integers and with and such that
Dirichlet's Approximation Theorem
See alsoHurwitz's Irrational Number Theorem, Irrationality Measure, Liouville's Approximation Theorem, Rational Approximation, Roth's Theorem
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ReferencesApostol, T. M. "Dirichlet's Approximation Theorem." §7.2 in Modular Functions and Dirichlet Series in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 143-145, 1997.
Referenced on Wolfram|AlphaDirichlet's Approximation Theorem
Cite this as:
Weisstein, Eric W. "Dirichlet's Approximation Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DirichletsApproximationTheorem.html