  This work provides a first step towards the construction of a noncommutative
geometry for the quantum Hall effect in the continuum. Taking inspiration from
the ideas developed by Bellissard during the 80's we build a spectral triple
for the $C^*$-algebra of continuous magnetic operators based on a Dirac
operator with compact resolvent. The metric aspects of this spectral triple are
studied, and an important piece of Bellissard's theory (the so-called first
Connes' formula) is proved.
