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Extend the symmedians of a triangle DeltaA_1A_2A_3 to meet the circumcircle at P_1, P_2, P_3. Then the symmedian point K of DeltaA_1A_2A_3 is also the symmedian point of ...

The cotangent bundle of a manifold is similar to the tangent bundle, except that it is the set (x,f) where x in M and f is a dual vector in the tangent space to x in M. The ...

Two non-coincident plane angles alpha and beta in angle standard position are said to be coterminal if the terminal side of alpha is identically the same as the terminal side ...

The numbers lambda_(nun) in the Gaussian quadrature formula Q_n(f)=sum_(nu=1)^nlambda_(nun)f(x_(nun)).

The cotree T^* of a spanning tree T in a connected graph G is the spacing subgraph of G containing exactly those edges of G which are not in T (Harary 1994, p. 39).

For a countable set of n disjoint events E_1, E_2, ..., E_n P( union _(i=1)^nE_i)=sum_(i=1)^nP(E_i).

A set function mu is said to possess countable subadditivity if, given any countable disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...

A counterexample is a form of counter proof. Given a hypothesis stating that F(x) is true for all x in S, show that there exists a b in S such that F(b) is false, ...

Let n objects be picked repeatedly with probability p_i that object i is picked on a given try, with sum_(i)p_i=1. Find the earliest time at which all n objects have been ...

Given n sets of variates denoted {X_1}, ..., {X_n} , the first-order covariance matrix is defined by V_(ij)=cov(x_i,x_j)=<(x_i-mu_i)(x_j-mu_j)>, where mu_i is the mean. ...