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A closed two-form omega on a complex manifold M which is also the negative imaginary part of a Hermitian metric h=g-iomega is called a Kähler form. In this case, M is called ...

Landau's problems are the four "unattackable" problems mentioned by Landau in the 1912 Fifth Congress of Mathematicians in Cambridge, namely: 1. The Goldbach conjecture, 2. ...

A 4-state two-dimensional Turing machine invented in the 1980s. The ant starts out on a grid containing black and white cells, and then follows the following set of rules. 1. ...

The nth root of the denominator B_n of the nth convergent A_n/B_n of a number x tends to a constant lim_(n->infty)B_n^(1/n) = e^beta (1) = e^(pi^2/(12ln2)) (2) = 3.275823... ...

In the fields of functional and harmonic analysis, the Littlewood-Paley decomposition is a particular way of decomposing the phase plane which takes a single function and ...

A geometric construction done with a movable compass alone. All constructions possible with a compass and straightedge are possible with a movable compass alone, as was ...

Minkowski's question mark function is the function y=?(x) defined by Minkowski for the purpose of mapping the quadratic surds in the open interval (0,1) into the rational ...

The nine-point center N (sometimes instead denoted F) is the center of the nine-point circle. It has equivalent triangle center functions alpha_5 = cos(B-C) (1) alpha_5 = ...

Given an arrangement of points, a line containing just two of them is called an ordinary line. Dirac (1951) conjectured that every sufficiently set of n noncollinear points ...

P is the point on the line AB such that PA^_/PB^_=1. It can also be thought of as the point of intersection of two parallel lines. In 1639, Desargues (1864) became the first ...