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In a graph G, contraction of an edge e with endpoints u,v is the replacement of u and v with a single vertex such that edges incident to the new vertex are the edges other ...

A group action G×X->X is effective if there are no trivial actions. In particular, this means that there is no element of the group (besides the identity element) which does ...

An illusion studied by the psychologist Walter Ehrenstein in which the sides of a square placed inside a pattern of concentric circles take an apparent curved shape. The name ...

Consider a point P inside a reference triangle DeltaABC, construct line segments AP, BP, and CP. The Ehrmann congruent squares point is the unique point P such that three ...

Let P be a matrix of eigenvectors of a given square matrix A and D be a diagonal matrix with the corresponding eigenvalues on the diagonal. Then, as long as P is a square ...

Let T be a central triangle and let U(T) be its unary cofactor triangle. Then T and U(T) are perspective, and their perspector is called the eigencenter of T. Let the A-, B-, ...

The surface of revolution given by the parametric equations x(u,v) = cosusin(2v) (1) y(u,v) = sinusin(2v) (2) z(u,v) = sinv (3) for u in [0,2pi) and v in [-pi/2,pi/2]. It is ...

A family of functors H_n(·) from the category of pairs of topological spaces and continuous maps, to the category of Abelian groups and group homomorphisms satisfies the ...

G_(ab)=R_(ab)-1/2Rg_(ab), where R_(ab) is the Ricci curvature tensor, R is the scalar curvature, and g_(ab) is the metric tensor. (Wald 1984, pp. 40-41). It satisfies ...

A graph G with m edges is said to be elegant if the vertices of G can be labeled with distinct integers (0,1,2,...,m) in such a way that the set of values on the edges ...