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In database structures, two quantities are generally of interest: the average number of comparisons required to 1. Find an existing random record, and 2. Insert a new random ...

A square which can be dissected into a number of smaller squares with no two equal is called a perfect square dissection (or a squared square). Square dissections in which ...

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 ...

Clean tile is a game investigated by Buffon (1777) in which players bet on the number of different tiles a thrown coin will partially cover on a floor that is regularly ...

The term "cylinder" has a number of related meanings. In its most general usage, the word "cylinder" refers to a solid bounded by a closed generalized cylinder (a.k.a. ...

In general, an icosidodecahedron is a 32-faced polyhedron. A number of such solids are illustrated above. "The" (quasiregular) icosidodecahedron is the 32-faced Archimedean ...

A Mrs. Perkins's quilt is a dissection of a square of side n into a number of smaller squares. The name "Mrs. Perkins's Quilt" comes from a problem in one of Dudeney's books, ...

A fractal which can be constructed using string rewriting beginning with a cell [1] and iterating the rules {0->[0 1 0; 1 1 1; 0 1 0],1->[1 1 1; 1 1 1; 1 1 1]}. (1) The size ...

Togliatti surfaces are quintic surfaces having the maximum possible number of ordinary double points (31). A related surface sometimes known as the dervish can be defined by ...

The n×n square matrix F_n with entries given by F_(jk)=e^(2piijk/n)=omega^(jk) (1) for j,k=0, 1, 2, ..., n-1, where i is the imaginary number i=sqrt(-1), and normalized by ...