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A spherical image of a curve. The most common indicatrix is Dupin's indicatrix.

The symmetry operation (x,y,z)->(-x,-y,-z). When used in conjunction with a rotation, it becomes an improper rotation.

A map which is monotone increasing and therefore order-preserving.

J_(nualphabeta)^mu=J_(nubetaalpha)^mu=1/2(R_(alphanubeta)^mu+R_(betanualpha)^mu), where R is the Riemann tensor.

The principal normal indicatrix of a closed space curve with nonvanishing curvature bisects the area of the unit sphere if it is embedded.

The symmetry operation (x,y,z)->(x,y,-z), etc., which is equivalent to 2^_, where the bar denotes an improper rotation.

A surface given by the form z=F(x,y).

An algebraic surface of degree 9. Enneper's minimal surface is an example of a nonic surface.

An angle which is not a right angle or a multiple of a right angle.

A nonsingular linear map A:R^n->R^n is orientation-reversing if det(A)<0.