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Two nonsingular forms are equivalent over the rationals iff they have the same determinant and the same p-signatures for all p.

The head of a vector AB^-> is the endpoint B, i.e., the point at which the arrow is placed.

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

An operator of period 2, i.e., an operator * which satisfies ((a)^*)^*=a.

An integral of motion which restricts the phase space available to a dynamical system.

The Jordan product of quantities x and y is defined by x·y=1/2(xy+yx).

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).

A mathematical structure (e.g., a group, vector space, or smooth manifold) in a category.

A geometry constructed without reference to measurement. The only primitive concepts are those of points and intermediacy. There are 10 axioms underlying ordered geometry.