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Let a_1, a_2, ..., a_n be scalars not all equal to 0. Then the set S consisting of all vectors X=[x_1; x_2; |; x_n] in R^n such that a_1x_1+a_2x_2+...+a_nx_n=c for c a ...

Hyperreal numbers are an extension of the real numbers to include certain classes of infinite and infinitesimal numbers. A hyperreal number x is said to be finite iff |x|<n ...

The hypersine (n-dimensional sine function) is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the ...

A space having dimension n>3.

The n-hypersphere (often simply called the n-sphere) is a generalization of the circle (called by geometers the 2-sphere) and usual sphere (called by geometers the 3-sphere) ...

In two dimensions, there are two periodic circle packings for identical circles: square lattice and hexagonal lattice. In 1940, Fejes Tóth proved that the hexagonal lattice ...

Marsaglia (1972) has given a simple method for selecting points with a uniform distribution on the surface of a 4-sphere. This is accomplished by picking two pairs of points ...

A hyperstring is a simple semi-Hamiltonian acyclic digraph (V,E) with a labeling of the edges in E such that, for all vertices i,j,p,q in V, either pi(i,j)=pi(p,q) or pi(i,j) ...

A generalization of an ordinary two-dimensional surface embedded in three-dimensional space to an (n-1)-dimensional surface embedded in n-dimensional space. A hypersurface is ...

The curve produced by fixed point P on the circumference of a small circle of radius b rolling around the inside of a large circle of radius a>b. A hypocycloid is therefore a ...