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A Kähler structure on a complex manifold M combines a Riemannian metric on the underlying real manifold with the complex structure. Such a structure brings together geometry ...

The pentagram, also called the five-point star, pentacle, pentalpha, or pentangle, is the star polygon {5/2}. It is a pagan religious symbol that is one of the oldest symbols ...

Find two distinct sets of integers {a_1,...,a_n} and {b_1,...,b_n}, such that for k=1, ..., m, sum_(i=1)^na_i^k=sum_(i=1)^nb_i^k. (1) The Prouhet-Tarry-Escott problem is ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

In finding the average area A^__R of a triangle chosen from a closed, bounded, convex region R of the plane, then A^__(T(R))=A^__R, for T any nonsingular affine ...

An arrangement of n>=3 points such that n-1 of them are collinear.

Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic. Formally, two graphs G and H with graph vertices ...

Mastermind is a simple two-player code-breaking board game invented in 1970 by Mordecai Meirowitz, an Israeli postmaster and telecommunications expert. It may have been ...

The biconjugate gradient method often displays rather irregular convergence behavior. Moreover, the implicit LU decomposition of the reduced tridiagonal system may not exist, ...

A statistical distribution published by William Gosset in 1908. His employer, Guinness Breweries, required him to publish under a pseudonym, so he chose "Student." Given N ...