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Draw antiparallels through the symmedian point K. The points where these lines intersect the sides then lie on a circle, known as the cosine circle (or sometimes the second ...

Cube duplication, also called the Delian problem, is one of the geometric problems of antiquity which asks, given the length of an edge of a cube, that a second cube be ...

Given relatively prime integers p and q (i.e., (p,q)=1), the Dedekind sum is defined by s(p,q)=sum_(i=1)^q((i/q))(((pi)/q)), (1) where ((x))={x-|_x_|-1/2 x not in Z; 0 x in ...

A Gaussian integer is a complex number a+bi where a and b are integers. The Gaussian integers are members of the imaginary quadratic field Q(sqrt(-1)) and form a ring often ...

The centroid is center of mass of a two-dimensional planar lamina or a three-dimensional solid. The mass of a lamina with surface density function sigma(x,y) is ...

Let N^* be the smallest dimension n of a hypercube such that if the lines joining all pairs of corners are two-colored for any n>=N^*, a complete graph K_4 of one color with ...

The process of finding a reduced set of basis vectors for a given lattice having certain special properties. Lattice reduction algorithms are used in a number of modern ...

Let T_1 be the point at which the J_1-excircle meets the side A_2A_3 of a triangle DeltaA_1A_2A_3, and define T_2 and T_3 similarly. Then the lines A_1T_1, A_2T_2, and A_3T_3 ...

Let DeltaH_AH_BH_C be the orthic triangle of a triangle DeltaABC. Then each side of each triangle meets the three sides of the other triangle, and the points of intersection ...

Given a point P, the pedal triangle of P is the triangle whose polygon vertices are the feet of the perpendiculars from P to the side lines. The pedal triangle of a triangle ...