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A space-filling function which maps a one-dimensional interval into a two-dimensional area. Plane-filling functions were thought to be impossible until Hilbert discovered the ...

The problem in calculus of variations to find the minimal surface of a boundary with specified constraints (usually having no singularities on the surface). In general, there ...

In its original form, the Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense) S^3, ...

The Poincaré hyperbolic disk is a two-dimensional space having hyperbolic geometry defined as the disk {x in R^2:|x|<1}, with hyperbolic metric ...

In Euclidean space R^3, the curve that minimizes the distance between two points is clearly a straight line segment. This can be shown mathematically as follows using ...

A point process is a probabilistic model for random scatterings of points on some space X often assumed to be a subset of R^d for some d. Oftentimes, point processes describe ...

Pong Hau K'i is an ancient Chinese tic-tac-toe-like game involving two players with two differently colored stones (say, red and blue). The players move their respective ...

A nonzero vector v=(v_0,v_1,...,v_(n-1)) in n-dimensional Lorentzian space R^(1,n-1) is said to be positive timelike if it has imaginary (Lorentzian) norm and if its first ...

For X a topological space, the presheaf F of Abelian groups (rings, ...) on X is defined such that 1. For every open subset U subset= X, an Abelian group (ring, ...) F(U), ...

The index I associated to a symmetric, non-degenerate, and bilinear g over a finite-dimensional vector space V is a nonnegative integer defined by I=max_(W in S)(dimW) where ...