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The radius of an excircle. Let a triangle have exradius r_A (sometimes denoted rho_A), opposite side of length a and angle A, area Delta, and semiperimeter s. Then r_1 = ...

A plane shape constructed by Reinhardt (1934) that is conjectured to be the "worst" packer of all centrally-symmetric plane regions. It has a packing density of ...

The placement of objects so that they touch in some specified manner, often inside a container with specified properties. For example, one could consider a sphere packing, ...

In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 ...

A directed graph is called an arborescence if, from a given node x known as the root vertex, there is exactly one elementary path from x to every other node y.

A weakly connected component of a simple directed graph (i.e., a digraph without loops) is a maximal subdigraph such that for every pair of distinct vertices u, v in the ...

Synergetics coordinates are a set of triangular coordinates in their plane (or their generalization to tetrahedral coordinates in space, or the analogs in higher dimensions). ...

Place two solid spheres of radius 1/2 inside a hollow sphere of radius 1 so that the two smaller spheres touch each other at the center of the large sphere and are tangent to ...

There are three types of cubic lattices corresponding to three types of cubic close packing, as summarized in the following table. Now that the Kepler conjecture has been ...

In general, the internal similitude center of two circles C_1=C(x_1,r_1) and C_2=C(x_2,r_2) with centers given in Cartesian coordinates is given by ...