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The placement of n points on a sphere so as to minimize the maximum distance of any point on the sphere from the closest one of the n points.

Tetrahedron picking is the process of picking tetrahedra at random within a given shape in 3 or higher dimensions. The most natural definition of a random tetrahedron is one ...

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 ...

For an ellipse given by the parametric equations x = acost (1) y = bsint, (2) the catacaustic is a complicated expression for generic radiant point (x_r,y_r). However, it ...

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 triangular graph T_n=L(K_n) is the line graph of the complete graph K_n (Brualdi and Ryser 1991, p. 152). The vertices of T_n may be identified with the 2-subsets of ...

A pyramid is a polyhedron with one face (known as the "base") a polygon and all the other faces triangles meeting at a common polygon vertex (known as the "apex"). A right ...

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 ...

In order to integrate a function over a complicated domain D, Monte Carlo integration picks random points over some simple domain D^' which is a superset of D, checks whether ...

The Nechushtan graph, illustrated above, is a 10-vertex 5-chromatic graph that is unit-distance in 3 dimensions. It was used by Nechushtan (2002) in the construction of of a ...