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In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 ...

A parallelian is a line drawn parallel to one side of a triangle. The three lines drawn through a given point are known as the triangle's parallelians. There exists a unique ...

The total number of contravariant and covariant indices of a tensor. The rank R of a tensor is independent of the number of dimensions N of the underlying space. An intuitive ...

The problem of finding the mean triangle area of a triangle with vertices picked inside a triangle with unit area was proposed by Watson (1865) and solved by Sylvester. It ...

A dragon curve is a recursive nonintersecting curve whose name derives from its resemblance to a certain mythical creature. The curve can be constructed by representing a ...

Game theory is a branch of mathematics that deals with the analysis of games (i.e., situations involving parties with conflicting interests). In addition to the mathematical ...

For a given m, determine a complete list of fundamental binary quadratic form discriminants -d such that the class number is given by h(-d)=m. Heegner (1952) gave a solution ...

The kite graph is the 5-vertex graph illustrated above (Brandstädt et al. 1987, p. 18). It is implemented in the Wolfram Language as GraphData["KiteGraph"]. Unfortunately, ...

Find the m×n array of single digits which contains the maximum possible number of primes, where allowable primes may lie along any horizontal, vertical, or diagonal line. For ...

Sociable numbers are numbers that result in a periodic aliquot sequence, where an aliquot sequence is the sequence of numbers obtained by repeatedly applying the restricted ...