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Teichmüller's theorem asserts the existence and uniqueness of the extremal quasiconformal map between two compact Riemann surfaces of the same genus modulo an equivalence ...

A number of attractive 8-compounds of the regular tetrahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

A simple unlabeled graph whose connectivity is considered purely on the basis of topological equivalence, so that two edges (v_1,v_2) and (v_2,v_3) joined by a node v_2 of ...

A surface of revolution obtained by rotating a closed plane curve about an axis parallel to the plane which does not intersect the curve. The simplest toroid is the torus. ...

Given n mutually exclusive events A_1, ..., A_n whose probabilities sum to unity, then P(B)=P(B|A_1)P(A_1)+...+P(B|A_n)P(A_n), where B is an arbitrary event, and P(B|A_i) is ...

To inscribe an equilateral triangle in an ellipse, place the top polygon vertex at (0,b), then solve to find the (x,y) coordinate of the other two vertices. ...

A unimodal sequence is a finite sequence that first increases and then decreases. A sequence {s_1,s_2,...,s_n} is unimodal if there exists a t such that s_1<=s_2<=...<=s_t ...

A square with side lengths 1. The unit square usually means the one with coordinates (0, 0), (1, 0), (1, 1), (0, 1) in the real plane, or 0, 1, 1+i, and i in the complex ...

The quantity which a function f takes upon application to a given quantity.

The system of partial differential equations (partial_t+partial_z^3+partial_(z^_)^3)v+partial_z(uv)+partial_(z^_)(vw) (1) partial_(z^_)u=3partial_zv (2) ...