Apparatus and methods for preparing a bone socket, such as the glenoid of the scapula, to receive a prosthetic component. The apparatus is an orthopedic instrument (reamer) used for the preparation of bone surface for the insertion of an implant. The reamer includes an elongate shaft, a connecting system (for example, a quick connect system), and a cutting head having a specific configuration, i.e., in the shape of a Nautilus shell having a logarithmic spiral. The cutting head is provided with a plurality of spokes that have different radii or lengths (that confer a non-constant non-uniform radius to the overall cutting head).
