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There are at least two meanings on the word congruent in mathematics. Two geometric figures are said to be congruent if one can be transformed into the other by an isometry ...

A product of ANDs, denoted ^ _(k=1)^nA_k. The conjunctions of a Boolean algebra A of subsets of cardinality p are the 2^p functions A_lambda= union _(i in lambda)A_i, where ...

A topological space decomposes into its connected components. The connectedness relation between two pairs of points satisfies transitivity, i.e., if a∼b and b∼c then a∼c. ...

A general mathematical property obeyed by mathematical objects in which all elements are within a neighborhood of nearby points. The continuous maps between topological ...

The winding number of a contour gamma about a point z_0, denoted n(gamma,z_0), is defined by n(gamma,z_0)=1/(2pii)∮_gamma(dz)/(z-z_0) and gives the number of times gamma ...

The phrase "convergence in mean" is used in several branches of mathematics to refer to a number of different types of sequential convergence. In functional analysis, ...

Let a, b, and c be the side lengths of a reference triangle DeltaABC. Now let A_b be a point on the extension of the segment CA beyond A such that AA_b=a. Similarly, define ...

A coordinate chart is a way of expressing the points of a small neighborhood, usually on a manifold M, as coordinates in Euclidean space. An example from geography is the ...

Given an affine variety V in the n-dimensional affine space K^n, where K is an algebraically closed field, the coordinate ring of V is the quotient ring ...

The corkscrew surface, sometimes also called the twisted sphere (Gray 1997, p. 477), is a surface obtained by extending a sphere along a diameter and then twisting. It can be ...