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Four-dimensional geometry is Euclidean geometry extended into one additional dimension. The prefix "hyper-" is usually used to refer to the four- (and higher-) dimensional ...

A tensor which has the same components in all rotated coordinate systems. All rank-0 tensors (scalars) are isotropic, but no rank-1 tensors (vectors) are. The unique rank-2 ...

The Johnson circumconic, a term used here for the first time, is the circumconic that passes through the vertices of both the reference triangle and the Johnson triangle. It ...

The Johnson triangle DeltaJ_AJ_BJ_C, a term coined here for the first time, is the triangle formed by the centers of the Johnson circles. It has trilinear vertex matrix ...

Lissajous curves are the family of curves described by the parametric equations x(t) = Acos(omega_xt-delta_x) (1) y(t) = Bcos(omega_yt-delta_y), (2) sometimes also written in ...

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 k-matching in a graph G is a set of k edges, no two of which have a vertex in common (i.e., an independent edge set of size k). Let Phi_k be the number of k-matchings of ...

The first theorem of Pappus states that the surface area S of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of ...

The triangle bounded by the polars of the vertices of a triangle DeltaABC with respect to a conic is called its polar triangle. The following table summarizes polar triangles ...

Three-dimensional generalization of the polyominoes to n dimensions. The number of polycubes N(n) composed of n cubes are 1, 1, 2, 8, 29, 166, 1023, ... (OEIS A000162; Ball ...