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Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined by these three points. The first ...

Coaxal circles are circles whose centers are collinear and that share a common radical line. The collection of all coaxal circles is called a pencil of coaxal circles ...

The constant a_(-1) in the Laurent series f(z)=sum_(n=-infty)^inftya_n(z-z_0)^n (1) of f(z) about a point z_0 is called the residue of f(z). If f is analytic at z_0, its ...

A set in R^n which can be reduced to one of its points, say P, by a continuous deformation, is said to be contractible. The transformation is such that each point of the set ...

A letter of the alphabet drawn with doubled vertical strokes is called doublestruck, or sometimes blackboard bold (because doublestruck characters provide a means of ...

An Enriques surface X is a smooth compact complex surface having irregularity q(X)=0 and nontrivial canonical sheaf K_X such that K_X^2=O_X (Endraß). Such surfaces cannot be ...

Let a closed surface have genus g. Then the polyhedral formula generalizes to the Poincaré formula chi(g)=V-E+F, (1) where chi(g)=2-2g (2) is the Euler characteristic, ...

Although the rigidity theorem states that if the faces of a convex polyhedron are made of metal plates and the polyhedron edges are replaced by hinges, the polyhedron would ...

The circumcircle of the Fuhrmann triangle. It has the line HNa, where H is the orthocenter and Na is the Nagel point, as its diameter. In fact, these points (Kimberling ...

The harmonic parameter of a polyhedron is the weighted mean of the distances d_i from a fixed interior point to the faces, where the weights are the areas A_i of the faces, ...