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If F is a family of more than n bounded closed convex sets in Euclidean n-space R^n, and if every H_n (where H_n is the Helly number) members of F have at least one point in ...

A subset S subset R^n is said to be pseudo-convex at a point x in S if the associated pseudo-tangent cone P_S(x) to S at x contains S-{x}, i.e., if S-{x} subset P_S(x). Any ...

The line on which the orthocenter H, triangle centroid G, circumcenter O, de Longchamps point L, nine-point center N, and a number of other important triangle centers lie. ...

Let P=alpha:beta:gamma be a point not on a sideline of a reference triangle DeltaABC. Let A^' be the point of intersection AP intersection BC, B^'=BP intersection AC, and ...

The Napoleon-Feuerbach cubic is the pivotal isogonal cubic with nine-point center N as the pivot point. It therefore has trilinear equation ...

Given a subset K of a vector space X, a nonempty subset S subset K is called an extreme set of K if no point of S is an internal point of any line interval whose endpoints ...

In floating-point arithmetic, a biased exponent is the result of adding some constant (called the bias) to the exponent chosen to make the range of the exponent nonnegative. ...

A perimeter-bisecting line segment which originates at a vertex of a polygon. The three splitters of a triangle concur in a point known as the Nagel point Na.

Each point in the convex hull of a set S in R^n is in the convex combination of n+1 or fewer points of S.

A family of subsets of a topological space such that every point has a neighborhood that intersects only one of them.