The Ge(110) surface reconstructs into ordered and disordered phases, in which the basic unit is a five-membered ring of Ge atoms (pentagon). The variety of surface reconstructions leads to a rich electronic density of states with several surface states. Using scanning tunneling microscopy and spectroscopy, we have identified the exact origins of these surface states and linked them to either the Ge pentagons or the underlying Ge-Ge bonds. We show that even moderate fluctuations in the positions of the Ge pentagonal units induce large variations in the local density of states. The local density of states modulates in a precise manner, following the geometrical constraints on tiling Ge pentagons. These geometry-correlated electronic states offer a vast configurational landscape that could provide new opportunities in data storage and computing applications.