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Any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal grid (i.e., the honeycomb, illustrated above). Pappus refers to the ...

The theta series of a lattice is the generating function for the number of vectors with norm n in the lattice. Theta series for a number of lattices are implemented in the ...

One of the eight convex deltahedra built up from 16 equilateral triangles. It consists of two oppositely faced square pyramids rotated 45 degrees to each other and separated ...

It is possible to construct simple functions which produce growing patterns. For example, the Baxter-Hickerson function f(n)=1/3(2·10^(5n)-10^(4n)+2·10^(3n)+10^(2n)+10^n+1) ...

A dipyramid with a square base. The octahedron is a special case of a square dipyramid with equal edge lengths. The volume of a square dipyramid with base edge lengths a and ...

A figurate number, also (but mostly in texts from the 1500 and 1600s) known as a figural number (Simpson and Weiner 1992, p. 587), is a number that can be represented by a ...

A fractal process for which H<1/2, so r<0.

Two slant triangular prisms fused together.

A cupola adjoined to a rotunda.

For n players, n-1 games are needed to fairly determine first place, and n-1+lg(n-1) are needed to fairly determine first and second place.