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A number n for which a shortest chain exists which is a Brauer chain is called a Brauer number. There are infinitely many non-Brauer numbers.

An interval in which one endpoint is included but not the other. A half-closed interval is denoted [a,b) or (a,b] and is also called a half-open interval. The non-standard ...

A set of methods that are generally superior to ANOVA for small data sets or where sample distributions are non-normal.

A transformation consisting of a constant offset with no rotation or distortion. In n-dimensional Euclidean space, a translation may be specified simply as a vector giving ...

A convex body in Euclidean space that is centrally symmetric with center at the origin is determined among all such bodies by its brightness function (the volume of each ...

The plane spanned by two coordinate axes in the three-dimensional Euclidean space. The coordinate plane spanned by the x- and the y-axis is called xy-plane.

Given a point P and a line AB, draw the perpendicular through P and call it PC. Let PD be any other line from P which meets CB in D. In a hyperbolic geometry, as D moves off ...

A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...

A polytope in n-dimensional Euclidean space R^n whose vertices are integer lattice points but which does not contain any other lattice points in its interior or on its ...

A mathematical property P holds locally if P is true near every point. In many different areas of mathematics, this notion is very useful. For instance, the sphere, and more ...