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A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex. A quadrilateral that can be both inscribed and ...

Linear programming, sometimes known as linear optimization, is the problem of maximizing or minimizing a linear function over a convex polyhedron specified by linear and ...

The general bivariate quadratic curve can be written ax^2+2bxy+cy^2+2dx+2fy+g=0. (1) Define the following quantities: Delta = |a b d; b c f; d f g| (2) J = |a b; b c| (3) I = ...

A vector is formally defined as an element of a vector space. In the commonly encountered vector space R^n (i.e., Euclidean n-space), a vector is given by n coordinates and ...

Pre-Calculus

A graph G is distance transitive if its automorphism group is transitive on pairs of vertices at each pairwise distance in the graph. Distance-transitivity is a ...

Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A ...

The absolute value of a real number x is denoted |x| and defined as the "unsigned" portion of x, |x| = xsgn(x) (1) = {-x for x<=0; x for x>=0, (2) where sgn(x) is the sign ...

Cartesian coordinates are rectilinear two- or three-dimensional coordinates (and therefore a special case of curvilinear coordinates) which are also called rectangular ...

Four circles c_1, c_2, c_3, and c_4 are tangent to a fifth circle or a straight line iff T_(12)T_(34)+/-T_(13)T_(42)+/-T_(14)T_(23)=0. (1) where T_(ij) is the length of a ...