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A Euclidean number is a number which can be obtained by repeatedly solving the quadratic equation. Euclidean numbers, together with the rational numbers, can be constructed ...

An Euler-Jacobi pseudoprime to a base a is an odd composite number n such that (a,n)=1 and the Jacobi symbol (a/n) satisfies (a/n)=a^((n-1)/2) (mod n) (Guy 1994; but note ...

A curve on the unit sphere S^2 is an eversion if it has no corners or cusps (but it may be self-intersecting). These properties are guaranteed by requiring that the curve's ...

A variation of chess involving a change in the form of the board, the rules of play, or the pieces used. For example, the normal rules of chess can be used but with a ...

The eigenvector corresponding to the second smallest eigenvalue (i.e., the algebraic connectivity) of the Laplacian matrix of a graph G. The Fiedler vector is used in ...

One of the beautiful arrangements of circles found at the Temple of Osiris at Abydos, Egypt (Rawles 1997). The pattern also appears in Phoenician art from the 9th century BC ...

In mathematics, a formula is a fact, rule, or principle that is expressed in terms of mathematical symbols. Examples of formulas include equations, equalities, identities, ...

Let n>=0 and alpha_1, alpha_2, ...be the positive roots of J_n(x)=0, where J_n(z) is a Bessel function of the first kind. An expansion of a function in the interval (0,1) in ...

The Fourier cosine transform of a real function is the real part of the full complex Fourier transform, F_x^((c))[f(x)](k) = R[F_x[f(x)](k)] (1) = ...

A Goldbach number is a positive integer that is the sum of two odd primes (Li 1999). Let E(x) (the "exceptional set of Goldbach numbers") denote the number of even numbers ...