In
mathematics,
orientability is a property of
surfaces in
Euclidean space that measures whether it is possible to make a consistent choice of
surface normal vector at every point. A choice of surface normal allows one to use the
right-hand rule to define a "clockwise" direction of loops in the surface, as needed by
Stokes' theorem for instance. More generally, orientability of an abstract surface, or
manifold, measures whether one can consistently choose a "clockwise" orientation for all loops in the manifold. Equivalently, a surface is
orientable if a two-dimensional figure such as in the space cannot be moved (continuously) around the space and back to where it started so that it looks like its own mirror image .