All Topics  
Length

 

 
   Email Print
   Bookmark   Link
 

 

Length
 
 
  Topics Length Topic Home

Length is the long dimension
Dimension

In mathematics, the dimension of a space is roughly defined as the minimum number of coordinates needed to specify every point within it. For example: a point on the unit circle in the plane can be specified by two Cartesian coordinates but one can make do with a single coordinate , so the circle is 1-dimensional even though it exists in...
 of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end. This may be distinguished from height
Height

Height is the measurement of vertical distance, but has two meanings in common use. It can either indicate how "tall" something is, or how "high up" it is....
, which is vertical extent, and width or breadth, which are the distance from side to side, measuring across the object at right angles to the length. In the physical sciences and engineering, the word "length" is typically used synonymously with "distance
Distance

Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria ....
", with symbol or .

Length is a measure of one dimension, whereas area
Area

Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The term surface area refers to the total area of the exposed surface of a 3-dimensional solid, such as the sum of the areas of the exposed sides of a polyhedron....
 is a measure of two dimensions (length squared) and volume
Volume

The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
 is a measure of three dimensions
Dimensions

Dimensions is a France project that makes educational movies about mathematics, focusing on Euclidean space. It uses POV-Ray to render some of the animations, and the films are release under a Creative Commons licence....
 (length cubed).






Discussion
Ask a question about 'Length'
Start a new discussion about 'Length'
Answer questions from other users
Full Discussion Forum



Encyclopedia


Length is the long dimension
Dimension

In mathematics, the dimension of a space is roughly defined as the minimum number of coordinates needed to specify every point within it. For example: a point on the unit circle in the plane can be specified by two Cartesian coordinates but one can make do with a single coordinate , so the circle is 1-dimensional even though it exists in...
 of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end. This may be distinguished from height
Height

Height is the measurement of vertical distance, but has two meanings in common use. It can either indicate how "tall" something is, or how "high up" it is....
, which is vertical extent, and width or breadth, which are the distance from side to side, measuring across the object at right angles to the length. In the physical sciences and engineering, the word "length" is typically used synonymously with "distance
Distance

Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria ....
", with symbol or .

Length is a measure of one dimension, whereas area
Area

Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The term surface area refers to the total area of the exposed surface of a 3-dimensional solid, such as the sum of the areas of the exposed sides of a polyhedron....
 is a measure of two dimensions (length squared) and volume
Volume

The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
 is a measure of three dimensions
Dimensions

Dimensions is a France project that makes educational movies about mathematics, focusing on Euclidean space. It uses POV-Ray to render some of the animations, and the films are release under a Creative Commons licence....
 (length cubed). In most systems of measurement, the unit of length is a fundamental unit
Fundamental unit

A set of fundamental units is a set of Units of measurement for physical quantity from which every other unit can be generated.In the language of measurement, quantities are quantifiable aspects of the world, such as time, distance, velocity, mass, momentum, energy, and weight, and units are used to describe their measure....
, from which other units are defined.

Units of length

In the physical sciences and engineering, when one speaks of "units of length", the word "length" is synonymous with "distance
Distance

Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria ....
". There are several units
Units of measurement

The definition, agreement and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day....
 that are used to measure
Measurement

Measurement is the process of assigning a number to an attribute according to a rule or set of rules. The term can also be used to refer to the result obtained after performing the process....
 length. Units of length
Unit of length

A unit of length is a way of measuring length or distance.Common units of length in the International System of Units are:* metre and its multiples, such as "centimetre" or "kilometre"...
 may be based on 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 fixed object.

In the International System of Units
International System of Units

The International System of Units is the modern form of the metric system and is generally a system devised around the convenience of the number ten....
 (SI), the basic unit
SI base unit

The International System of Units defines seven dimensional analysis SI base units. All other physical units can be derived from these base units: these are known as SI derived units....
 of length is the metre
Metre

The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes....
 and is now defined in terms of the speed of light
Speed of light

The speed of light in an free space is an important physical constant usually written as c, with a value of 299,792,458 metres per second....
. The centimetre
Centimetre

A centimetre is a Units of measurement of length in the metric system, equal to one hundredth of a metre, which is the current International System of Units SI base unit of length....
 and the kilometre
Kilometre

The kilometre , symbol km is a Units of measurement of length in the metric system, equal to one thousand metres.Slang terms for kilometre include click and kay ....
, derived from the metre, are also commonly used units. In U.S. customary units, English or Imperial system of units, commonly used units of length are the inch
Inch

An inch is the name of a Units of measurement of length in a number of different systems, including Imperial units, and United States customary units....
, the foot, the yard
Yard

A yard is a Units of measurement of length in several different systems, including English units, Imperial units, and United States customary units....
, and the mile
Mile

A mile is a Units of measurement of length, usually used to measure distance, in a number of different systems. In contemporary English contexts, mile most commonly refers to the statute mile of 5,280 Feet or the nautical mile of 1,852 meters ....
.

Units used to denote distances in the vastness of space, as in astronomy
Astronomy

Astronomy is the science of Astronomical object and Phenomenon that originate outside the Earth's atmosphere . It is concerned with the evolution, physics, chemistry, meteorology, and motion of celestial objects, as well as the physical cosmology....
, are much longer than those typically used on Earth and include the astronomical unit
Astronomical unit

An astronomical unit is a unit of length based on the mean distance from the Earth to the Sun. The precise value of the AU is currently accepted as 149,597,870,691 Plus-minus sign 6 metres ....
, the light-year
Light-year

A light-year or light year is a Units of measurement of length, equal to just under ten orders_of_magnitude_%28numbers%29#1012 kilometres....
, and the parsec
Parsec

The parsec is a units of measurement of astronomical units of length, equal to just under 31 orders_of_magnitude_#1012 kilometres , or about 3.26 light-years....
.

Units used to denote microscopically small distances, as in chemistry
Chemistry

Chemistry is the science concerned with the composition, structure, and properties of matter, as well as the changes it undergoes during chemical reactions....
, include the micron and the ångström
Ångström

An ?ngstr?m or angstrom is an internationally recognized non-SI unit of length equal to 0.1 nanometre or 1 metres. It is sometimes used in expressing the sizes of atoms, lengths of chemical bonds and optical spectrum, and dimensions of parts of integrated circuits....
.

Length of moving rods

While the length of a resting rod can be measured by direct comparison with a measuring rod, this comparison cannot be performed while the rod is moving, due to relativistic concerns
Length contraction

Length contraction, according to Hendrik Lorentz, is the physical phenomenon of a decrease in length detected by an observer in objects that travel at any non-zero velocity relative to that observer....
. In this case we define its moving length as the distance between its two endpoints at a given instance.

If the world line
World line

In physics, the world line of an object is the unique path of that object as it travels through 4-dimensional spacetime.The concept of "world line" is distinguished from the concept of "orbit" or "trajectory" by the time dimension, and typically encompasses a large area of spacetime wherein perception straight paths are recalculated to...
s of the two endpoints of the rod expressed in the coordinates of an inertial reference frame are



and



then the length of the rod in this reference frame at the instance is



Since in special relativity
Special relativity

Special relativity is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein in the paper "Annus Mirabilis Papers#Special relativity"....
 the relation of simultaneity
Relativity of simultaneity

The relativity of simultaneity is the concept that simultaneity is not absolute, but dependent on the observer. That is, according to the special theory of relativity formulated by Albert Einstein in 1905, it is impossible to say in an absolute sense whether two events occur at the same time if those events are separated in space....
 depends on the chosen frame of reference, the length of moving rods also depends.

Generalizations

In the differential geometry of curves
Differential geometry of curves

Differential geometry of curves is the branch of geometry that dealswith smooth curve in the Euclidean plane and in the Euclidean space by methods of differential calculus and integral calculus....
 and differential geometry of surfaces
Differential geometry of surfaces

In mathematics, the differential geometry of surfaces deals with smooth manifold surfaces with various additional structures, most often, a Riemannian metric....
, length is an important global Riemannian
Riemannian geometry

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, manifold with a Riemannian metric, i.e. with an inner product on the tangent space at each point which varies smooth function from point to point....
 invariant
Invariant

Invariant and invariance may have several meanings, among which are:* Invariant , an expression whose value doesn't change during execution ...
.

See also

  • Distance
    Distance

    Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria ....
  • Dimension
    Dimension

    In mathematics, the dimension of a space is roughly defined as the minimum number of coordinates needed to specify every point within it. For example: a point on the unit circle in the plane can be specified by two Cartesian coordinates but one can make do with a single coordinate , so the circle is 1-dimensional even though it exists in...
  • Orders of magnitude (length)
    Orders of magnitude (length)

    To help compare different orders of magnitude, the following list describes various lengths between 1.6 m and 1.3 m.|}Detailed List...
  • Contains a chapter giving the history of length and angle measurement.
  • Smoot
    Smoot

    The smoot is a List of strange units of measurement unit of length created as part of an Massachusetts Institute of Technology hazing. It is named after Oliver R....
  • Unit of length
    Unit of length

    A unit of length is a way of measuring length or distance.Common units of length in the International System of Units are:* metre and its multiples, such as "centimetre" or "kilometre"...