Search Results for ""

A cube whose edge lengths are 1. The unit cube therefore has unit volume.

The following vector integrals are related to the curl theorem. If F=cxP(x,y,z), (1) then int_CdsxP=int_S(daxdel )xP. (2) If F=cF, (3) then int_CFds=int_Sdaxdel F. (4) The ...

A smooth two-dimensional surface given by embedding the projective plane into projective 5-space by the homogeneous parametric equations v(x,y,z)=(x^2,y^2,z^2,xy,xz,yz). The ...

The great dirhombicosidodecahedron is the uniform polyhedron with Maeder index 75 (Maeder 1997), Wenninger index 119 (Wenninger 1989), Coxeter index 82 (Coxeter et al. 1954), ...

A point process is a probabilistic model for random scatterings of points on some space X often assumed to be a subset of R^d for some d. Oftentimes, point processes describe ...

A polyhedron dissection (or decomposition) is a dissection of one or more polyhedra into other shapes. Two polyhedra can be dissected into each other iff they have equal Dehn ...

Every smooth nonzero vector field on the 3-sphere has at least one closed orbit. The conjecture was proposed in 1950 and proved true for Hopf maps. The conjecture was ...

There are at least two distinct notions of when a point process is stationary. The most commonly utilized terminology is as follows: Intuitively, a point process X defined on ...

For every even dimension 2n, the symplectic group Sp(2n) is the group of 2n×2n matrices which preserve a nondegenerate antisymmetric bilinear form omega, i.e., a symplectic ...

The tetragonal antiwedge is the topological class of hexahedron. It has 10 edges and 6 vertices and its faces consist of 4 triangles and 2 quadrilaterals. A tetragonal ...