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In Book IX of The Elements, Euclid gave a method for constructing perfect numbers (Dickson 2005, p. 3), although this method applies only to even perfect numbers. In a 1638 ...

The "15 puzzle" is a sliding square puzzle commonly (but incorrectly) attributed to Sam Loyd. However, research by Slocum and Sonneveld (2006) has revealed that Sam Loyd did ...

Consider the probability Q_1(n,d) that no two people out of a group of n will have matching birthdays out of d equally possible birthdays. Start with an arbitrary person's ...

The generalized minimal residual (GMRES) method (Saad and Schultz 1986) is an extension of the minimal residual method (MINRES), which is only applicable to symmetric ...

The Mittag-Leffler function (Mittag-Leffler 1903, 1905) is an entire function defined by the series E_alpha(z)=sum_(k=0)^infty(z^k)/(Gamma(alphak+1)) (1) for alpha>0. It is ...

The term "snark" was first popularized by Gardner (1976) as a class of minimal cubic graphs with edge chromatic number 4 and certain connectivity requirements. (By Vizing's ...

Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions ...

An amicable pair (m,n) consists of two integers m,n for which the sum of proper divisors (the divisors excluding the number itself) of one number equals the other. Amicable ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

The divisor function sigma_k(n) for n an integer is defined as the sum of the kth powers of the (positive integer) divisors of n, sigma_k(n)=sum_(d|n)d^k. (1) It is ...