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The regulator of a number field K is a positive number associated with K. The regulator of an imaginary quadratic field is 1 and that of a real quadratic, imaginary cubic, or ...

A polygon whose vertices do not all lie in a plane.

Every dense linear order complete set without endpoints having at most omega disjoint intervals is order isomorphic to the continuum of real numbers, where omega is the set ...

The south pole is the point on a sphere with minimum z-coordinate for a given coordinate system. For a rotating sphere like the Earth, the natural coordinate system is ...

Tetrahedron picking is the process of picking tetrahedra at random within a given shape in 3 or higher dimensions. The most natural definition of a random tetrahedron is one ...

f(x)=1-2x^2 for x in [-1,1]. Fixed points occur at x=-1, 1/2, and order 2 fixed points at x=(1+/-sqrt(5))/4. The natural invariant of the map is rho(y)=1/(pisqrt(1-y^2)).

An ultrametric is a metric which satisfies the following strengthened version of the triangle inequality, d(x,z)<=max(d(x,y),d(y,z)) for all x,y,z. At least two of d(x,y), ...

A parallelogram (parallelepiped) containing the minimum repeatable elements of a circle (sphere) packing.

The system of partial differential equations (partial_t+partial_z^3+partial_(z^_)^3)v+partial_z(uv)+partial_(z^_)(vw) (1) partial_(z^_)u=3partial_zv (2) ...

A polygon whose interior consists of all points in the plane which are closer to a particular lattice point than to any other. The generalization to n dimensions is called a ...