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The vectors +/-a_1, ..., +/-a_n in a three-space form a normalized eutactic star iff Tx=x for all x in the three-space.

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.

Let the sum of the squares of the digits of a positive integer s_0 be represented by s_1. In a similar way, let the sum of the squares of the digits of s_1 be represented by ...

The smallest nontrivial taxicab number, i.e., the smallest number representable in two ways as a sum of two cubes. It is given by 1729=1^3+12^3=9^3+10^3. The number derives ...

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|.

A database accessed by one or more hash functions.