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A bubble is a minimal-energy surface of the type that is formed by soap film. The simplest bubble is a single sphere, illustrated above (courtesy of J. M. Sullivan). More ...

In plane geometry, a chord is the line segment joining two points on a curve. The term is often used to describe a line segment whose ends lie on a circle. The term is also ...

A uniform distribution of points on the circumference of a circle can be obtained by picking a random real number between 0 and 2pi. Picking random points on a circle is ...

A conical frustum is a frustum created by slicing the top off a cone (with the cut made parallel to the base). For a right circular cone, let s be the slant height and R_1 ...

There are a number of attractive polyhedron compounds involving four cubes, several of which are illustrated above. The first (left figures), also known as Bakos' compound, ...

A number of attractive cube 6-compounds can be constructed. A first (left figures) is obtained by combining six cubes, each rotated by 1/6 of a turn about the line joining ...

Instead of picking two points from the interior of the cube, instead pick two points on different faces of the unit cube. In this case, the average distance between the ...

The great truncated cuboctahedron (Maeder 1997), also called the quasitruncated cuboctahedron (Wenninger 1989, p. 145), is the uniform polyhedron with Maeder index 20 (Maeder ...

The great truncated icosidodecahedron, also called the great quasitruncated icosidodecahedron, is the uniform polyhedron with Maeder index 68 (Maeder 1997), Wenninger index ...

A hexagon tiling is a tiling of the plane by identical hexagons. The regular hexagon forms a regular tessellation, also called a hexagonal grid, illustrated above. There are ...