  We find the exact value of the best possible constant $C$ for the weak type
$(1,1)$ inequality for the one dimensional centered Hardy-Littlewood maximal
operator. We prove that $C$ is the largest root of the quadratic equation
$12C^{2}-22C+5=0$ thus obtaining $C=1.5675208...$. This is the first time the
best constant for one of the fundamental inequalities satisfied by a centered
maximal operator is precisely evaluated.

Classical Analysis and ODEs