Markov constant

Markov constant of a number
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Domain, codomain and image
Domain	Irrational numbers
Codomain	Lagrange spectrum with ${\displaystyle \infty }$
Basic features
Parity	even
Period	1
Specific values
Maxima	${\displaystyle +\infty }$
Minima	√5
Value at ${\displaystyle \phi }$	√5
Value at √2	2√2
This function is undefined on rationals; hence, it is not continuous.

In number theory, specifically in Diophantine approximation theory, the Markov constant ${\displaystyle M(\alpha )}$ of an irrational number ${\displaystyle \alpha }$ is the factor for which Dirichlet's approximation theorem can be improved for ${\displaystyle \alpha }$.