Definition:Lagrange Number

Definition
Let $\xi$ be an irrational number.

Consider a real number $L_n$ such that there are infinitely many relatively prime integers $p, q \in \Z$ such that:


 * $\size {\xi - \dfrac p q} < \dfrac 1 {L_n q^2}$

We define the Lagrange number of $\xi$ to be $\map L \xi = \map \sup L$ over all $L$ satisfying the inequality above.

Also known as
This is also referred to in some sources as a Markov Constant.

Also see

 * Liouville's Theorem (Number Theory)
 * Hurwitz's Theorem (Number Theory)