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A group action G×X->X is called free if, for all x in X, gx=x implies g=I (i.e., only the identity element fixes any x). In other words, G×X->X is free if the map G×X->X×X ...

A homogeneous space M is a space with a transitive group action by a Lie group. Because a transitive group action implies that there is only one group orbit, M is isomorphic ...

A Steiner system S(t,k,v) is a set X of v points, and a collection of subsets of X of size k (called blocks), such that any t points of X are in exactly one of the blocks. ...

The value nearest to but still inside an inner fence.

The plane through an edge of a trihedron drawn perpendicularly to the opposite face. The term was first used by J. Neuberg (Altshiller-Court 1979, p. 298).

The augmented truncated tetrahedron is Johnson solid J_(65) constructed by affixing a triangular cupola to one of the hexagonal faces of a truncated tetrahedron such that the ...

Given a function f(x) plotted in the Cartesian plane as y=f(x), the average rate of change (or average rate of change function) of f from x to a is given by ...

All triangles are bicentric, i.e., possess both an incircle and a circumcircle. This is not necessarily the case for polygons with four or more sides. The inradius r and ...

One name for the figure used by Euclid to prove the Pythagorean theorem. It is sometimes also known as the "windmill."

The collapsoids are a class of non-convex collapsible polyhedra. They can be constructed by replacing each edge of a dodecahedron or icosahedron by the diagonal of a pyramid ...