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If the square is instead erected internally, their centers form a triangle DeltaI_AI_BI_C that has (exact) trilinear vertex matrix given by (1) (E. Weisstein, Apr. 25, 2004). ...

Let P(z) and Q(z) be univariate polynomials in a complex variable z, and let the polynomial degrees of P and Q satisfy deg(Q)>=deg(P+2). Then int_gamma(P(z))/(Q(z))dz = ...

The Lucas central triangle (a term coined here for the first time) is the triangle DeltaL_AL_BL_C formed by the centers of the Lucas circles of a given reference triangle ...

The outer Napoleon triangle is the triangle DeltaN_C^'N_B^'N_A^' formed by the centers of externally erected equilateral triangles DeltaABE_C^', DeltaACE_B^', and ...

By analogy with the outer Napoleon triangle, consider the external erection of three squares on the sides of a triangle DeltaABC. These centers form a triangle DeltaO_AO_BO_C ...

A sutured manifold is a tool in geometric topology which was first introduced by David Gabai in order to study taut foliations on 3-manifolds. Roughly, a sutured manifold is ...

Any bounded planar region with positive area >A placed in any position of the unit square lattice can be translated so that the number of lattice points inside the region ...

The circum-orthic triangle DeltaA^'B^'C^' is the circumcevian triangle of a triangle DeltaABC with respect to the orthocenter H (Kimberling 1998, p. 163). The circum-orthic ...

A metric space X which is not complete has a Cauchy sequence which does not converge. The completion of X is obtained by adding the limits to the Cauchy sequences. For ...

Let n points xi_1, ..., xi_n be randomly distributed on a domain S, and let H be some event that depends on the positions of the n points. Let S^' be a domain slightly ...