bundle(redirected from Arnold bundle)
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in mathematics, a two-parameter family of curves in the plane or in space that are linear functions of the parameters. Suppose F1, F2, and F3 are functions of two variables and none of the functions is a linear combination of the other two. The family of curves in the plane that are determined by the equation
(*) λ1F1 + λ2F2 + λ3F3 = 0
for all possible values of the parameters λ1, λ2, and λ3 (except for the case λ1 = 0, λ2 = 0, and λ3 = 0) constitutes a bundle. Equation (*) is in fact a function of two parameters—that is, of the two ratios λ1: λ2: λ3. In addition, it is immediately apparent that the parameters occur in this equation linearly. The equation of a bundle of surfaces in space is formed analogously. The three equations F1 = 0, F2 = 0, and F3 = 0 yield three elements of the bundle (three curves of three surfaces), which determine the entire bundle.
Bundles are usually considered whose elements are similar in certain respects; examples are a bundle of circles and a bundle of planes. We sometimes also speak of a bundle of lines in space; although the bundle is considered in space, its elements are curves rather than surfaces. Nevertheless, this case can be reduced to the case of a bundle of planes, since the pairwise intersections of elements of a bundle of planes determine a set of lines. In projective geometry, a bundle is understood to mean both sets—lines and planes—at once.
bundle(1) To sell hardware and software as a combined product or to combine several software packages for sale as a single unit. Contrast with unbundle. See bundled software and bundling.
(2) A collection of files that are treated as one. See APP file.