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A catenary of revolution. The catenoid and plane are the only surfaces of revolution which are also minimal surfaces. The catenoid can be given by the parametric equations x ...

There are several attractive polyhedron compounds consisting of three cubes. The first (left figures) arises by joining three cubes such that each shares two C_2 axes (Holden ...

An equilateral zonohedron is a zonohedron in which the line segments of the star on which it is based are of equal length (Coxeter 1973, p. 29). Plate II (following p. 32 of ...

The generalized law of sines applies to a simplex in space of any dimension with constant Gaussian curvature. Let us work up to that. Initially in two-dimensional space, we ...

An edge-magic graph is a labeled graph with e graph edges labeled with distinct elements {1,2,...,e} so that the sum of the graph edge labels at each graph vertex is the ...

The Poincaré hyperbolic disk is a two-dimensional space having hyperbolic geometry defined as the disk {x in R^2:|x|<1}, with hyperbolic metric ...

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 random walk is a sequence of discrete steps in which each step is randomly taken subject to some set of restrictions in allowed directions and step lengths. Random walks ...

Differential Geometry

An almost integer is a number that is very close to an integer. Near-solutions to Fermat's last theorem provide a number of high-profile almost integers. In the season 7, ...