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A method for predicting the onset of widespread chaos.

A three-dimensional coordinate system in which the axes satisfy the right-hand rule.

An algebra with no nontrivial nilpotent ideals. In the 1890s, Cartan, Frobenius, and Molien independently proved that any finite-dimensional semisimple algebra over the real ...

A shuffle-exchange graph is a nonsimple graph (due to the existence of graph loops) whose vertices are length n binary strings with an edge from w to w^' if 1. w^' differs ...

The nth-order Sierpiński tetrahedron graph is the connectivity graph of black triangles in the nth iteration of the tetrix fractal. The first three iterations are shown ...

A three-dimensional knot spun about a plane in four dimensions. Unlike suspended knots, spun knots are smoothly embedded at the poles.

A set that is a smooth embedded two-dimensional manifold except for a subset that consists of smooth embedded curves, except for a set of isolated points.

Let x be a point in an n-dimensional compact manifold M, and attach at x a copy of R^n tangential to M. The resulting structure is called the tangent space of M at x and is ...

Coordinates useful for plotting projective three-dimensional curves of the form f(x_0,x_1,x_2,x_3)=0 which are defined by x_0 = 1-z-sqrt(2)x (1) x_1 = 1-z+sqrt(2)x (2) x_2 = ...

Due to Lebesgue and Brouwer. If an n-dimensional figure is covered in any way by sufficiently small subregions, then there will exist points which belong to at least n+1 of ...