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A category modeled after the properties of the category of sets. A category E is a topos if E has finite limits and every object of E has a power object (Barr and Wells 1985, ...

Let G(V,E) be a graph with graph vertices V and graph edges E on n graph vertices without a (k+1)-clique. Then t(n,k)<=((k-1)n^2)/(2k), where t(n,k) is the edge count. (Note ...

A formal type of proof most frequently encountered in elementary geometry courses in which known or derived statements are written in the left column, and the reason that ...

A circuit in which an entire graph is traversed in one route. Examples of curves that can be traced unicursally are the Mohammed sign and unicursal hexagram. The numbers of ...

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 ...

A volume element is the differential element dV whose volume integral over some range in a given coordinate system gives the volume of a solid, V=intintint_(G)dxdydz. (1) In ...

Two polygons are congruent by dissection iff they have the same area. In particular, any polygon is congruent by dissection to a square of the same area. Laczkovich (1988) ...

A web diagram, also called a cobweb plot, is a graph that can be used to visualize successive iterations of a function y=f(x). In particular, the segments of the diagram ...

Given a positive nondecreasing sequence 0<lambda_1<=lambda_2<=..., the zeta-regularized product is defined by product_(n=1)^^^inftylambda_n=exp(-zeta_lambda^'(0)), where ...

Trigonometry