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Any set of n+2 points in R^n can always be partitioned in two subsets V_1 and V_2 such that the convex hulls of V_1 and V_2 intersect.

For a set partition of n elements, the n-character string a_1a_2...a_n in which each character gives the set block (B_0, B_1, ...) in which the corresponding element belongs ...

The d-dimensional rigidity matrix M(G) of a graph G with vertex count n, edge count m in the variables v_i=(x_1,...,x_d) is the m×(dn) matrix with rows indexed by the edges ...

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...

The study of figures on the surface of a sphere (such as the spherical triangle and spherical polygon), as opposed to the type of geometry studied in plane geometry or solid ...

The combination of a central dilation and a rotation about the same center. However, the combination of a central dilation and a rotation whose centers are distinct is also a ...

A subgraph G^' of a graph G is a graph G^' whose vertex set and edge set are subsets of those of G. If G^' is a subgraph of G, then G is said to be a supergraph of G^' ...

A symmetric function on n variables x_1, ..., x_n is a function that is unchanged by any permutation of its variables. In most contexts, the term "symmetric function" refers ...

Given a triangle with angles (pi/p, pi/q, pi/r), the resulting symmetry group is called a (p,q,r) triangle group (also known as a spherical tessellation). In three ...

A vector field is a map f:R^n|->R^n that assigns each x a vector f(x). Several vector fields are illustrated above. A vector field is uniquely specified by giving its ...