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A pair of numbers m and n such that sigma^*(m)=sigma^*(n)=m+n, where sigma^*(n) is the unitary divisor function. Hagis (1971) and García (1987) give 82 such pairs. The first ...

Universal algebra studies common properties of all algebraic structures, including groups, rings, fields, lattices, etc. A universal algebra is a pair A=(A,(f_i^A)_(i in I)), ...

Four circles may be drawn through an arbitrary point P on a torus. The first two circles are obvious: one is in the plane of the torus and the second perpendicular to it. The ...

Voronin (1975) proved the remarkable analytical property of the Riemann zeta function zeta(s) that, roughly speaking, any nonvanishing analytic function can be approximated ...

The term "wedge" has a number of different meanings in mathematics. It is sometimes used as another name for the caret symbol. The term also refers to the notation ( ^ ) used ...

A famous perceptual illusion in which the brain switches between seeing a young girl and an old woman (or "wife" and "mother in law"). An anonymous German postcard from 1888 ...

The first of the Hardy-Littlewood conjectures. The k-tuple conjecture states that the asymptotic number of prime constellations can be computed explicitly. In particular, ...

Given a Hilbert space H, a *-subalgebra A of B(H) is said to be a von Neumann algebra in H provided that A is equal to its bicommutant A^('') (Dixmier 1981). Here, B(H) ...

666 is the occult "number of the beast," also called the "sign of the devil" (Wang 1994), associated in the Bible with the Antichrist. It has figured in many numerological ...

The first Brocard point is the interior point Omega (also denoted tau_1 or Z_1) of a triangle DeltaABC with points labeled in counterclockwise order for which the angles ...