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If J is a simple closed curve in R^2, the closure of one of the components of R^2-J is homeomorphic with the unit 2-ball. This theorem may be proved using the Riemann mapping ...

An algorithm that can always be used to decide whether a given polynomial is free of zeros in the closed unit disk (or, using an entire linear transformation, to any other ...

The second Morley cubic is the triangle cubic with trilinear equation It passes through Kimberling centers X_n for n=1, 1134, 1135, 1136, and 1137.

The nth-order Sierpiński tetrahedron graph is the connectivity graph of black triangles in the nth iteration of the tetrix fractal. The first three iterations are shown ...

A sigma-compact topological space is a topological space that is the union of countably many compact subsets.

The socle of a group G is the subgroup generated by its minimal normal subgroups. For example, the symmetric group S_4 has two nontrivial normal subgroups: A_4 and ...

The image on the Riemann sphere of any circle under a complex rational mapping with numerator and denominator having degrees no more than n has length no longer than 2npi.

A polynomial equation whose roots all have negative real parts. For a real quadratic equation z^2+Bz+C=0, the stability conditions are B,C>0. For a real cubic equation ...

An expression built up from statements letters by appropriate application of connectives (Mendelson 1997, p. 13).

In the triangle DeltaABC illustrated above, side c subtends angle ∠C. More generally, given a geometric object O in the plane and a point P, let A be the angle from one edge ...