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A curve and its polar reciprocal with regard to the fixed conic have the same Halphen transformation.

A system of variables which can be written in the form of Hamilton's equations.

The rules for the multiplication of quaternions.

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

A right-angled parallelepiped with dimensions a×ab×abc, where a, b, and c are integers.

A polynomial function of the elements of a vector x can be uniquely decomposed into a sum of harmonic polynomials times powers of |x|.

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

An associative ring, also called a Hecke ring, which has a technical definition in terms of commensurable subgroups.

A 100-sided polygon, virtually indistinguishable in appearance from a circle except at very high magnification.

The vertical length of an object from top to bottom.