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An irreducible fraction is a fraction p/q for which GCD(p,q)=1, i.e., p and q are relatively prime. For example, in the complex plane, (4+7i)/(2+i)=3+2i is reducible, while ...

The word polyhedron has slightly different meanings in geometry and algebraic geometry. In geometry, a polyhedron is simply a three-dimensional solid which consists of a ...

If f is continuous on a closed interval [a,b], and c is any number between f(a) and f(b) inclusive, then there is at least one number x in the closed interval such that ...

The Jacobi theta functions are the elliptic analogs of the exponential function, and may be used to express the Jacobi elliptic functions. The theta functions are ...

The bias of a series is defined as Q[a_i,a_(i+1),a_(i+2)]=(a_ia_(i+2)-a_(i+1)^2)/(a_ia_(i+1)a_(i+2)). A series is geometric iff Q=0. A series is artistic iff the bias is ...

If f is continuous on a closed interval [a,b], then there is at least one number x^* in [a,b] such that int_a^bf(x)dx=f(x^*)(b-a). The average value of the function (f^_) on ...

The term Euclidean refers to everything that can historically or logically be referred to Euclid's monumental treatise The Thirteen Books of the Elements, written around the ...

Sylvester's four-point problem asks for the probability q(R) that four points chosen at random in a planar region R have a convex hull which is a quadrilateral (Sylvester ...

A triple (a,b,c) of positive integers satisfying a<b<c is said to be harmonic if 1/a+1/c=2/b. In particular, such a triple is harmonic if the reciprocals of its terms form an ...

If a continuous function defined on an interval is sometimes positive and sometimes negative, it must be 0 at some point. Bolzano (1817) proved the theorem (which effectively ...