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A cubic map is three-colorable iff each interior region is bounded by an even number of regions. A non-cubic map bounded by an even number of regions is not necessarily ...

Construct a 5×5×5 cube from thirteen 1×2×4 blocks, one 2×2×2 block, one 1×2×2, and three 1×1×3 blocks.

A polycube composed of 5 cubes. There are 29 distinct three-dimensional pentacubes (Bouwkamp 1981). Of these, the 12 planar pentacubes (corresponding to solid pentominoes), ...

Assemble six 1×2×2 blocks and three 1×1×1 blocks into a 3×3×3 cube.

Place a point somewhere on a line segment. Now place a second point and number it 2 so that each of the points is in a different half of the line segment. Continue, placing ...

In 1803, Malfatti posed the problem of determining the three circular columns of marble of possibly different sizes which, when carved out of a right triangular prism, would ...

Minkowski's conjecture states that every lattice tiling of R^n by unit hypercubes contains two hypercubes that meet in an (n-1)-dimensional face. Minkowski first considered ...

In most modern literature, a Boolean model is a probabilistic model of continuum percolation theory characterized by the existence of a stationary point process X and a ...

The Boy surface is a nonorientable surface that is one possible parametrization of the surface obtained by sewing a Möbius strip to the edge of a disk. Two other ...

A division algebra, also called a "division ring" or "skew field," is a ring in which every nonzero element has a multiplicative inverse, but multiplication is not ...