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Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. [1] It is also known as Lorentz contraction or Lorentz–FitzGerald contraction (after Hendrik Lorentz and George Francis FitzGerald ) and is usually only noticeable ...
A contraction mapping has at most one fixed point. Moreover, the Banach fixed-point theorem states that every contraction mapping on a non-empty complete metric space has a unique fixed point, and that for any x in M the iterated function sequence x , f ( x ), f ( f ( x )), f ( f ( f ( x ))), ... converges to the fixed point.
For example, a curve in a metric space is rectifiable (has finite length) if and only if it has a Lipschitz reparametrization. A 1-Lipschitz map is sometimes called a nonexpanding or metric map. Metric maps are commonly taken to be the morphisms of the category of metric spaces. A K-Lipschitz map for K < 1 is called a contraction.
The so-called Length contraction without expansion perpendicularly to the line of motion and by the precise value = / (where l 0 is the length at rest in the aether) was given by Larmor in 1897 and by Lorentz in 1904. In the same year, Lorentz also argued that electrons themselves are also affected by this contraction.
This glossary of geography terms is a list of definitions of terms and concepts used in geography and related fields, including Earth science, oceanography, cartography, and human geography, as well as those describing spatial dimension, topographical features, natural resources, and the collection, analysis, and visualization of geographic ...
For example, the perimeter of a regular polygon inscribed in a circle approaches the circumference with increasing numbers of sides (and decrease in the length of one side). In geometric measure theory such a smooth curve as the circle that can be approximated by small straight segments with a definite limit is termed a rectifiable curve . [ 7 ]
Crystallography is one of the traditional areas of geology that use mathematics. Crystallographers make use of linear algebra by using the Metrical Matrix. The Metrical Matrix uses the basis vectors of the unit cell dimensions to find the volume of a unit cell, d-spacings, the angle between two planes, the angle between atoms, and the bond ...
Glossary of geography terms may refer to: Glossary of geography terms (A–M) Glossary of geography terms (N–Z) This page was last edited on 25 ...