nonorientate

Nonorientate is a nonstandard term in mathematics and philosophy. In mathematical usage, the property commonly described is nonorientability; "nonorientate" may appear as a verb in some writings, but the standard adjective is nonorientable or not orientable. When used as a verb, it would mean to render something unable to admit a global orientation, but such usage is rare.

In topology, a manifold is orientable if it admits a globally consistent choice of orientation for its tangent spaces. If no such global orientation can be chosen, the manifold is nonorientable. Locally, the manifold may possess an orientation, but transporting a local orientation around certain loops reverses it, preventing a single global orientation. Classic examples of nonorientable surfaces are the Möbius strip, the real projective plane, and the Klein bottle. By contrast, orientable surfaces include the sphere and the torus.

The concept is important in fields such as geometry and physics, where orientation affects how certain integrals are defined and how symmetry and parity are treated. In common English, orientate is sometimes used as a synonym for orient, and nonorientate would be unusual outside specific technical contexts. For mathematical discussion, it is more precise to refer to orientation as a property and to label objects as orientable or nonorientable.

See also: orientable, nonorientable, Möbius strip, Klein bottle, real projective plane, orientation.