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A rigorous mathematical argument which unequivocally demonstrates the truth of a given proposition. A mathematical statement that has been proven is called a theorem. ...

A quantified system of real algebraic equations and inequalities in variables {x_1,...,x_n} is an expression QS=Q_1(y_1)Q_2(y_2)...Q_m(y_m)S(x_1,...,x_n;y_1,...,y_m), where Q ...

A generalization of Ramsey theory to mathematical objects in which one would not normally expect structure to be found. For example, there exists a graph with very few ...

Let CD be the altitude of a triangle DeltaABC and let E be its midpoint. Then area(DeltaABC)=1/2AB·CD=AB·DE, and ABFG can be squared by rectangle squaring. The general ...

A witness is a number which, as a result of its number theoretic properties, guarantees either the compositeness or primality of a number n. Witnesses are most commonly used ...

An array of "trees" of unit height located at integer-coordinate points in a point lattice. When viewed from a corner along the line y=x in normal perspective, a quadrant of ...

The point of concurrence S of a triangle's cleavers M_1C_1, M_2C_2, and M_3C_3, which is simply the Spieker center, i.e., the incenter of the medial triangle DeltaM_1M_2M_3 ...

The symbol used in continental Europe, most of North and South America (with the exception of the United States and Canada), and most of Africa to denote a decimal point, for ...

The Schoute center is the inverse of the symmedian point in the circumcircle. It has triangle center function alpha_(187)=a(2a^2-b^2-c^2) and corresponds to Kimberling center ...

Given a real m×n matrix A, there are four associated vector subspaces which are known colloquially as its fundamental subspaces, namely the column spaces and the null spaces ...