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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 ...

A relation expressing a sum potentially involving binomial coefficients, factorials, rational functions, and power functions in terms of a simple result. Thanks to results by ...

The German mathematician Kronecker proved that all the Galois extensions of the rationals Q with Abelian Galois groups are subfields of cyclotomic fields Q(mu_n), where mu_n ...

In 1611, Kepler proposed that close packing (either cubic or hexagonal close packing, both of which have maximum densities of pi/(3sqrt(2)) approx 74.048%) is the densest ...

Consider a convex pentagon and extend the sides to a pentagram. Externally to the pentagon, there are five triangles. Construct the five circumcircles. Each pair of adjacent ...

An outlier is an observation that lies outside the overall pattern of a distribution (Moore and McCabe 1999). Usually, the presence of an outlier indicates some sort of ...

Sprague (1963) considered the problem of "rolling" five cubes, each which an upright letter "A" on its top, on a chessboard. Here "rolling" means the cubes are moved from ...

The S distribution is defined in terms of its distribution function F(x) as the solution to the initial value problem (dF)/(dx)=alpha(F^g-F^h), where F(x_0)=F_0 (Savageau ...

The Shaw Prizes are $1 million cash awards offered annually by Run Run Shaw (b. 1907), a longtime movie and television producer. There are prizes for astronomy, life science ...

A four-sided quadrilateral not contained in a plane. The lines connecting the midpoints of opposite sides of a skew quadrilateral intersect (and bisect) each other (Steinhaus ...