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A multimagic square such that the first, second, third, and fourth powers of the elements all yield magic squares is known as a tetramagic square. The first known tetramagic ...

The illusion due to psychologist Edward Bradford Titchener that a circle surrounded by other circles will appear smaller if the surrounding circles are enlarged. This effect ...

Following Yates (1980), a prime p such that 1/p is a repeating decimal with decimal period shared with no other prime is called a unique prime. For example, 3, 11, 37, and ...

Delta(x_1,...,x_n) = |1 x_1 x_1^2 ... x_1^(n-1); 1 x_2 x_2^2 ... x_2^(n-1); | | | ... |; 1 x_n x_n^2 ... x_n^(n-1)| (1) = product_(i,j; i>j)(x_i-x_j) (2) (Sharpe 1987). For ...

For a given point lattice, some number of points will be within distance d of the origin. A Waterman polyhedron is the convex hull of these points. A progression of Waterman ...

Whipple derived a great many identities for generalized hypergeometric functions, many of which are consequently known as Whipple's identities (transformations, etc.). Among ...

x^n=sum_(k=0)^n<n; k>(x+k; n), where <n; k> is an Eulerian number and (n; k) is a binomial coefficient (Worpitzky 1883; Comtet 1974, p. 242).

The Zeckendorf representation of a positive integer n is a representation of n as a sum of nonconsecutive distinct Fibonacci numbers, n=sum_(k=2)^Lepsilon_kF_k, where ...

Differential Equations

A graph whose nodes are sequences of symbols from some alphabet and whose edges indicate the sequences which might overlap. The above figures show the first few n-dimensional ...