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Divide a triangle by its three medians into six smaller triangles. Surprisingly, the circumcenters O_(AB), O_(BA), etc. of the six circumcircles of these smaller triangles ...

The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric ...

The curve a hanging flexible wire or chain assumes when supported at its ends and acted upon by a uniform gravitational force. The word catenary is derived from the Latin ...

A (finite, circular) conical surface is a ruled surface created by fixing one end of a line segment at a point (known as the vertex or apex of the cone) and sweeping the ...

A constant, sometimes also called a "mathematical constant," is any well-defined real number which is significantly interesting in some way. In this work, the term "constant" ...

There are a number of attractive polyhedron compounds consisting of five cubes. The first of these (left figures) consists of the arrangement of five cubes in the polyhedron ...

Cubic graphs, also called trivalent graphs, are graphs all of whose nodes have degree 3 (i.e., 3-regular graphs). Cubic graphs on n nodes exists only for even n (Harary 1994, ...

The Kirchhoff sum index KfS is a graph index defined for a graph on n nodes by KfS=1/2sum_(i=1)^nsum_(j=1)^n((Omega)_(ij))/((d)_(ij)), where (Omega)_(ij) is the resistance ...

Mastermind is a simple two-player code-breaking board game invented in 1970 by Mordecai Meirowitz, an Israeli postmaster and telecommunications expert. It may have been ...

Nonstandard analysis is a branch of mathematical logic which introduces hyperreal numbers to allow for the existence of "genuine infinitesimals," which are numbers that are ...