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dtau^2=-eta_(alphabeta)dxi^alphadxi^beta, or (d^2xi^alpha)/(dtau^2)=0.

The goat problem (or bull-tethering problem) considers a fenced circular field of radius a with a goat (or bull, or other animal) tied to a point on the interior or exterior ...

Objects which are identical except for a mirror reflection are said to display handedness and to be chiral.

The locus of a point which is derived from a fixed point Q by continuous parallel displacement.

A curve created by starting with a circle, dividing it into six arcs, and flipping three alternating arcs. The process is then repeated an infinite number of times.

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.