In
mathematics, the
Klein bottle is an example of a
non-orientable surface; it is a
two-dimensional manifold against which a system for determining a
normal vector cannot be consistently defined. Informally, it is a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. Other related non-orientable objects include the
Möbius strip and the
real projective plane. Whereas a Möbius strip is a surface with
boundary, a Klein bottle has no boundary (for comparison, a
sphere is an orientable surface with no boundary).