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There does not exist an everywhere nonzero tangent vector field on the 2-sphere S^2. This implies that somewhere on the surface of the Earth, there is a point with zero ...

A closed three-dimensional figure (which may, according to some terminology conventions, be self-intersecting). Kern and Bland (1948, p. 18) define a solid as any limited ...

An equilibrium minimal surface for a crystal or drop which has the least anisotropic surface free energy for a given volume. It is the anisotropic analog of a sphere. In the ...

A handle is a topological structure which can be thought of as the object produced by puncturing a surface twice, attaching a zip around each puncture travelling in opposite ...

The solid angle Omega subtended by a surface S is defined as the surface area Omega of a unit sphere covered by the surface's projection onto the sphere. This can be written ...

The n-ball, denoted B^n, is the interior of a sphere S^(n-1), and sometimes also called the n-disk. (Although physicists often use the term "sphere" to mean the solid ball, ...

Let M be a compact n-dimensional manifold with injectivity radius inj(M). Then Vol(M)>=(c_ninj(M))/pi, with equality iff M is isometric to the standard round sphere S^n with ...

A random number generator produced by iterating X_(n+1)=|100lnX_n (mod 1)| for a seed X_0=0.1. This simple generator passes the noise sphere test for randomness by showing no ...

The real projective plane with elliptic metric where the distance between two points P and Q is defined as the radian angle between the projection of the points on the ...

The interior of a set is the union of all its open subsets. More informally, the interior of geometric structure is that portion of a region lying "inside" a specified ...