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Let the speed sigma of a closed curve on the unit sphere S^2 never vanish. Then the tangent indicatrix, also called the tantrix, tau=(sigma^.)/(|sigma^.|) is another closed ...

The polyhedron compound of the truncated octahedron and its dual, the tetrakis hexahedron. The compound can be constructed from a truncated octahedron of unit edge length by ...

The compound of a truncated tetrahedron and its dual, the triakis tetrahedron. The compound can be constructed from a truncated octahedron of unit edge length by midpoint ...

To each epsilon>0, there corresponds a delta such that ||f-g||<epsilon whenever ||f||=||g||=1 and ||(f+g)/2||>1-delta. This is a geometric property of the unit sphere of ...

A square with side lengths 1. The unit square usually means the one with coordinates (0, 0), (1, 0), (1, 1), (0, 1) in the real plane, or 0, 1, 1+i, and i in the complex ...

v=(dr)/(dt), (1) where r is the radius vector and d/dt is the derivative with respect to time. Expressed in terms of the arc length, v=(ds)/(dt)T^^, (2) where T^^ is the unit ...

Let f be a family of meromorphic functions on the unit disk D which are not normal at 0. Then there exist sequences f_n in F, z_n, rho_n, and a nonconstant function f ...

A perfect magic cube is a magic cube for which the rows, columns, pillars, space diagonals, and diagonals of each n×n orthogonal slice sum to the same number (i.e., the magic ...

Ball point picking is the selection of points randomly placed inside a ball. n random points can be picked in a unit ball in the Wolfram Language using the function ...

Ball tetrahedron picking is the selection of quadruples of points (corresponding to vertices of a general tetrahedron) randomly placed inside a ball. n random tetrahedra can ...