Length is commonly understood to mean the most extendeddimension of a fixed object.[1] However, this is not always the case and may depend on the position the object is in.
Various terms for the length of a fixed object are used, and these includeheight, which is vertical length or vertical extent, width, breadth, and depth.Height is used when there is a base from which vertical measurements can be taken.Width andbreadth usually refer to a shorter dimension thanlength.Depth is used for the measure of athird dimension.[2]
Length is the measure of one spatial dimension, whereasarea is a measure of two dimensions (length squared) andvolume is a measure of three dimensions (length cubed).
Measurement has been important ever since humans settled from nomadic lifestyles and started using building materials, occupying land and trading with neighbours. As trade between different places increased, the need for standard units of length increased. And later, as society has become more technologically oriented, much higher accuracy of measurement is required in an increasingly diverse set of fields, from micro-electronics to interplanetary ranging.[3]
UnderEinstein'sspecial relativity, length can no longer be thought of as being constant in allreference frames. Thus aruler that is one metre long in one frame of reference will not be one metre long in a reference frame that is moving relative to the first frame. This means the length of an object varies depending on the speed of the observer.
In Euclidean geometry, length is measured alongstraight lines unless otherwise specified and refers tosegments on them.Pythagoras's theorem relating the length of the sides of aright triangle is one of many applications in Euclidean geometry. Length may also be measured along other types of curves and is referred to asarclength.
In atriangle, the length of analtitude, a line segment drawn from a vertexperpendicular to the side not passing through the vertex (referred to as abase of the triangle), is called the height of the triangle.
Thearea of arectangle is defined to be length × width of the rectangle. If a long thin rectangle is stood up on its short side then its area could also be described as its height × width.
In other geometries, length may be measured along possibly curved paths, calledgeodesics. TheRiemannian geometry used ingeneral relativity is an example of such a geometry. Inspherical geometry, length is measured along thegreat circles on the sphere and the distance between two points on the sphere is the shorter of the two lengths on the great circle, which is determined by the plane through the two points and the center of the sphere.
In measure theory, length is most often generalized to general sets of via theLebesgue measure. In the one-dimensional case, the Lebesgue outer measure of a set is defined in terms of the lengths of open intervals. Concretely, the length of anopen interval is first defined as
so that the Lebesgue outer measure of a general set may then be defined as[6]
In the physical sciences and engineering, when one speaks ofunits of length, the wordlength is synonymous withdistance. There are severalunits that are used tomeasure length. Historically, units of length may have been derived from the lengths of human body parts, the distance travelled in a number of paces, the distance between landmarks or places on the Earth, or arbitrarily on the length of some common object.
Units used to denote distances in the vastness of space, as inastronomy, are much longer than those typically used on Earth (metre or kilometre) and include theastronomical unit (au), thelight-year, and theparsec (pc).
Units used to denote sub-atomic distances, as innuclear physics, are much smaller than the millimetre. Examples include thefermi (fm).
