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A Lie group is a smooth manifold obeying the group properties and that satisfies the additional condition that the group operations are differentiable. This definition is ...

Let L denote the n×n square lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L such ...

Let E be a compact connected subset of d-dimensional Euclidean space. Gross (1964) and Stadje (1981) proved that there is a unique real number a(E) such that for all x_1, ...

A nexus number is a figurate number built up of the nexus of cells less than n steps away from a given cell. The nth d-dimensional nexus number is given by N_d(n) = ...

Perspective is the art and mathematics of realistically depicting three-dimensional objects in a two-dimensional plane, sometimes called centric or natural perspective to ...

A space-filling function which maps a one-dimensional interval into a two-dimensional area. Plane-filling functions were thought to be impossible until Hilbert discovered the ...

The set of fixed points which do not move as a knot is transformed into itself is not a knot. The conjecture was proved in 1978 (Morgan and Bass 1984). According to Morgan ...

A vector basis of a vector space V is defined as a subset v_1,...,v_n of vectors in V that are linearly independent and span V. Consequently, if (v_1,v_2,...,v_n) is a list ...

A vector space V is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space R^n, where every element ...

The tensor product of two vector spaces V and W, denoted V tensor W and also called the tensor direct product, is a way of creating a new vector space analogous to ...