Definition:Lagrange Number

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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


Source of Name

This entry was named for Joseph Louis Lagrange.


Sources