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The volumes of any n n-dimensional solids can always be simultaneously bisected by a (n-1)-dimensional hyperplane. Proving the theorem for n=2 (where it is known as the ...

A surface of revolution defined by Kepler. It consists of more than half of a circular arc rotated about an axis passing through the endpoints of the arc. The equations of ...

Any one of the eight Apollonius circles of three given circles is tangent to a circle H known as a Hart circle, as are the other three Apollonius circles having (1) like ...

A meromorphic function is a single-valued function that is analytic in all but possibly a discrete subset of its domain, and at those singularities it must go to infinity ...

There are at least two integrals called the Poisson integral. The first is also known as Bessel's second integral, ...

The number of regions into which space can be divided by n mutually intersecting spheres is N=1/3n(n^2-3n+8), giving 2, 4, 8, 16, 30, 52, 84, ... (OEIS A046127) for n=1, 2, ...

A spheroid is an ellipsoid having two axes of equal length, making it a surface of revolution. By convention, the two distinct axis lengths are denoted a and c, and the ...

Given a triangle with angles (pi/p, pi/q, pi/r), the resulting symmetry group is called a (p,q,r) triangle group (also known as a spherical tessellation). In three ...

There are three types of cubic lattices corresponding to three types of cubic close packing, as summarized in the following table. Now that the Kepler conjecture has been ...

A barrel solid of revolution composed of parallel circular top and bottom with a common axis and a side formed by a smooth curve symmetrical about the midplane. The term also ...