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In 1750, Benjamin Franklin constructed the above 8×8 semimagic square having magic constant 260. Any half-row or half-column in this square totals 130, and the four corners ...

Let G be a k-regular graph with girth 5 and graph diameter 2. (Such a graph is a Moore graph). Then, k=2, 3, 7, or 57. A proof of this theorem is difficult (Hoffman and ...

Homogeneous barycentric coordinates are barycentric coordinates normalized such that they become the actual areas of the subtriangles. Barycentric coordinates normalized so ...

Let P be a primitive polytope with eight vertices. Then there is a unimodular map that maps P to the polyhedron whose vertices are (0, 0, 0), (1, 0, 0), (0, 1, 0), (0, 0, 1), ...

The icositruncated dodecadodecahedron, also called the icosidodecatruncated icosidodecahedron, is the uniform polyhedron with Maeder index 45 (Maeder 1997), Wenninger index ...

A fractal derived from the Koch snowflake. The base curve and motif for the fractal are illustrated below. The area enclosed by pieces of the curve after the nth iteration is ...

In the field of functional analysis, the Krein-Milman theorem is a result which characterizes all (nonempty) compact convex subsets K of "sufficiently nice" topological ...

An attractive tiling of the square composed of two types of triangular tiles. It consists of 16 equilateral triangles and 32 15 degrees-15 degrees-150 degrees isosceles ...

The limaçon trisectrix is a trisectrix that is a special case of the rose curve with n=1/3 (possibly with translation, rotation, and scaling). It was studied by Archimedes, ...

A lion and a man in a closed arena have equal maximum speeds. What tactics should the lion employ to be sure of his meal? This problem was stated by Rado in 1925 (Littlewood ...