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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 ...

A topological space X fulfils the T1-separation axiom and is normal. A space fulfilling the T_4-separation axiom is said to be a T4-space.

A number of attractive 26-compounds of the regular tetrahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

The third Lemoine circle, a term coined here for the first time, is the circumcircle of the Lemoine triangle. It has center function alpha=(f(a,b,c))/a, (1) where f(a,b,c) is ...

A lamp is turned on for 1/2 minute, off for 1/4 minute, on for 1/8 minute, etc. At the end of one minute, the lamp switch will have been moved aleph_0 times, where aleph_0 is ...

A three-colorable graph G is a graph with chromatic number chi(G)<=3.