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The insphere of a solid is a sphere that is tangent to all faces of the solid. An insphere does not always exist, but when it does, its radius r is called the inradius and ...

An orientation on an n-dimensional manifold is given by a nowhere vanishing differential n-form. Alternatively, it is an bundle orientation for the tangent bundle. If an ...

There exist lattices in n dimensions having hypersphere packing densities satisfying eta>=(zeta(n))/(2^(n-1)), where zeta(n) is the Riemann zeta function. However, the proof ...

The equation x_1^2+x_2^2+...+x_n^2-2x_0x_infty=0 represents an n-dimensional hypersphere S^n as a quadratic hypersurface in an (n+1)-dimensional real projective space ...

Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In three-dimensional Euclidean space, parallel lines not only fail to ...

Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In three-dimensional Euclidean space, parallel lines not only fail to ...

Given an open subset U in n-dimensional space and two compact subsets C_0 and C_1 of U, where C_1 is derived from C_0 by a continuous motion, is it possible to move C_0 to ...

Consider an n-dimensional deterministic dynamical system x^_^.=f^_(x) and let S be an n-1-dimensional surface of section that is traverse to the flow, i.e., all trajectories ...

A polytope in four dimensions. Polychora are bounded by polyhedra.

In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...