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Let P be the principal (initial investment), r be the annual compounded rate, i^((n)) the "nominal rate," n be the number of times interest is compounded per year (i.e., the ...

Ellipses sharing common foci (left figure). The family of confocal ellipses covers the plane simply, in the sense that there is a unique ellipse passing through each point in ...

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 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 ...

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 ...