# Dictionary Definition

distance

### Noun

1 the property created by the space between two
objects or points

2 a distant region; "I could see it in the
distance"

3 size of the gap between two places; "the
distance from New York to Chicago"; "he determined the length of
the shortest line segment joining the two points" [syn: length]

4 indifference by personal withdrawal; "emotional
distance" [syn: aloofness]

5 the interval between two times; "the distance
from birth to death"; "it all happened in the space of 10 minutes"
[syn: space]

6 a remote point in time; "if that happens it
will be at some distance in the future"; "at a distance of ten
years he had forgotten many of the details"

### Verb

1 keep at a distance; "we have to distance
ourselves from these events in order to continue living"

2 go far ahead of; "He outdistanced the other
runners" [syn: outdistance, outstrip]

# User Contributed Dictionary

## English

### Pronunciation

- /ˈdɪstəns/

### Noun

- The amount of
space between two points, usually geographical
points, usually (but not necessarily) measured along a straight line.
- The distance to Petersborough is thirty miles.

- In the context of "uncountable|figurative": The entire amount of space to the objective.
- He had promised to perform this task, but did not go the distance.

- In the context of "uncountable|figurative": A considerable
amount of space.
- The friendship did not survive the row: they kept each other at a distance.

#### Derived terms

#### Related terms

#### Translations

amount of space between two points

- Breton: pellder -ioù p
- Catalan: distància
- Czech: vzdálenost
- Dutch: afstand
- Esperanto: distanco
- Finnish: etäisyys
- French: distance
- German: Distanz, Entfernung, Abstand
- Hebrew: מרחק
- Indonesian: jarak
- Interlingua: distantia
- Italian: distanza
- Japanese: 距離
- Korean: 거리 [距離] (geori)
- Lithuanian: nuotolis, atstumas, sometimes distancija
- Malayalam: ദൂരം (dooram), അകലം (akalam)
- Polish: odległość, droga, dystans
- Portuguese: distância
- Romanian: distanţă
- Slovene: razdalja (1)
- Spanish: distancia
- Swedish: avstånd, distans
- Telugu: దూరము

#### See also

### Verb

- To move away from someone or something.

#### Translations

move away

- Breton: pellaat diouzh, mont diouzh
- Dutch: verwijderen
- Finnish: etäännyttää
- German: entfernen
- Hebrew: להתרחק (lehitrakheq)
- Indonesian: menjauhi
- Interlingua: distantiar
- Polish: dystansować się
- Portuguese: distanciar-se, afastar-se
- Romanian: distanţa
- Spanish: alejar-se
- Swedish: distansera sig, avlägsna sig

## French

### Pronunciation

- /dis'tɔ̃s(ə)/

### Noun

fr-noun f#### Derived terms

# Extensive Definition

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 (e.g. "two counties over"). In
mathematics,
distance must meet more rigorous criteria.

In most cases there is symmetry and "distance
from A to B" is interchangeable with "distance between B and
A".

## Mathematics

### Geometry

In neutral geometry, the minimum distance between two points is the length of the line segment between them.In analytic
geometry, the distance between two points of the
xy-plane can be found using the distance formula. The distance
between (x1, y1) and (x2, y2) is given by

- d=\sqrt=\sqrt.\,

Similarly, given points (x1, y1, z1) and (x2, y2,
z2) in
three-space, the distance between them is

- d=\sqrt=\sqrt.

In the study of complicated geometries, we call
this (most common) type of distance Euclidean
distance, as it is derived from the Pythagorean
theorem, which does not hold in Non-Euclidean
geometries. This distance formula can also be expanded
into the arc-length
formula.

### Distance in Euclidean space

In the Euclidean
space Rn, the distance between two points is usually given by
the Euclidean
distance (2-norm distance). Other distances, based on other
norms,
are sometimes used instead.

For a point (x1, x2, ...,xn) and a point (y1, y2,
...,yn), the Minkowski distance of order p (p-norm distance) is
defined as: p need not be an integer, but it cannot be less than 1,
because otherwise the triangle
inequality does not hold.

The 2-norm distance is the Euclidean
distance, a generalization of the Pythagorean
theorem to more than two coordinates. It is what
would be obtained if the distance between two points were measured
with a ruler: the
"intuitive" idea of distance.

The 1-norm distance is more colourfully called
the taxicab norm or Manhattan
distance, because it is the distance a car would drive in a
city laid out in square blocks (if there are no one-way
streets).

The infinity norm distance is also called
Chebyshev
distance. In 2D it represents the distance kings must
travel between two squares on a chessboard.

The p-norm is rarely used for values of p other
than 1, 2, and infinity, but see; super
ellipse.

In physical space the Euclidean distance is in a
way the most natural one, because in this case the length of a
rigid
body does not change with rotation.

### General case

In mathematics, in particular geometry, a distance function on a given set M is a function d: M×M → R, where R denotes the set of real numbers, that satisfies the following conditions:- d(x,y) ≥ 0, and d(x,y) = 0 if and only if x = y. (Distance is positive between two different points, and is zero precisely from a point to itself.)
- It is symmetric: d(x,y) = d(y,x). (The distance between x and y is the same in either direction.)
- It satisfies the triangle inequality: d(x,z) ≤ d(x,y) + d(y,z). (The distance between two points is the shortest distance along any path).

For example, the usual definition of distance
between two real numbers x and y is: d(x,y) = |x − y|. This
definition satisfies the three conditions above, and corresponds to
the standard topology
of the real
line. But distance on a given set is a definitional choice.
Another possible choice is to define: d(x,y) = 0 if x = y, and 1
otherwise. This also defines a metric, but gives a completely
different topology, the "discrete
topology"; with this definition numbers cannot be arbitrarily
close.

### Distances between sets and between a point and a set

Various distance definitions are possible between objects. For example, between celestial bodies one should not confuse the surface-to-surface distance and the center-to-center distance. If the former is much less than the latter, as for a LEO, the first tends to be quoted (altitude), otherwise, e.g. for the Earth-Moon distance, the latter.There are two common definitions for the distance
between two non-empty subsets of a given set:

- One version of distance between two non-empty sets is the infimum of the distances between any two of their respective points, which is the every-day meaning of the word. This is a symmetric prametric. On a collection of sets of which some touch or overlap each other, it is not "separating", because the distance between two different but touching or overlapping sets is zero. Also it is not hemimetric, i.e., the triangle inequality does not hold, except in special cases. Therefore only in special cases this distance makes a collection of sets a metric space.
- The Hausdorff distance is the larger of two values, one being the supremum, for a point ranging over one set, of the infimum, for a second point ranging over the other set, of the distance between the points, and the other value being likewise defined but with the roles of the two sets swapped. This distance makes the set of non-empty compact subsets of a metric space itself a metric space.

The is the infimum of the distances between the
point and those in the set. This corresponds to the distance,
according to the first-mentioned definition above of the distance
between sets, from the set containing only this point to the other
set.

In terms of this, the definition of the Hausdorff
distance can be simplified: it is the larger of two values, one
being the supremum, for a point ranging over one set, of the
distance between the point and the set, and the other value being
likewise defined but with the roles of the two sets swapped.

## Distance versus displacement

Distance cannot be negative.
Distance is a scalar
quantity, containing only a magnitude,
whereas displacement
is an equivalent vector
quantity containing both magnitude and
direction.

The distance covered by a vehicle (often recorded
by an odometer),
person, animal, object, etc. should be distinguished from the
distance from starting point to end point, even if latter is taken
to mean e.g. the shortest distance along the road, because a detour
could be made, and the end point can even coincide with the
starting point.

## Other "distances"

- Mahalanobis distance is used in statistics.
- Hamming distance is used in coding theory.
- Levenshtein distance
- Chebyshev distance

## See also

- Taxicab geometry
- astronomical units of length
- cosmic distance ladder
- comoving distance
- distance geometry
- distance (graph theory)
- Distance in military affairs
- Dijkstra's algorithm
- distance-based road exit numbers
- Distance Measuring Equipment (DME)
- great-circle distance
- length
- milestone
- Metric (mathematics)
- Metric space
- orders of magnitude (length)
- Proper length
- distance matrix
- Hamming distance
- proxemics - physical distance between people

## References

- E. Deza, M.M. Deza, Dictionary of Distances, Elsevier (2006) ISBN 0-444-52087-2

distance in Arabic: مسافة

distance in Bulgarian: Разстояние

distance in Catalan: Distància

distance in Czech: Vzdálenost

distance in Danish: Distance

distance in German: Abstand

distance in Modern Greek (1453-): Απόσταση

distance in Spanish: Distancia

distance in Esperanto: Distanco

distance in Basque: Luzera

distance in French: Distance
(mathématiques)

distance in Galician: Distancia

distance in Korean: 거리

distance in Ido: Disto

distance in Indonesian: Jarak

distance in Interlingua (International Auxiliary
Language Association): Distantia

distance in Icelandic: Fjarlægðarformúlan

distance in Italian: Distanza

distance in Luxembourgish: Ofstand

distance in Malay (macrolanguage): Jarak

distance in Dutch: Afstand

distance in Japanese: 距離

distance in Polish: Odległość

distance in Portuguese: Distância

distance in Russian: Расстояние

distance in Simple English: Distance

distance in Slovak: Vzdialenosť

distance in Slovenian: Razdalja

distance in Swedish: Avstånd

distance in Thai: ระยะทาง

distance in Vietnamese: Khoảng cách

distance in Urdu: فاصلہ (ریاضی)

distance in Yiddish: ווייטקייט

distance in Chinese: 距离

distance in Finnish: Välimatka

# Synonyms, Antonyms and Related Words

aloofness, ambit, amplitude, angle, area, arena, back, backdrop, background, backwardness, base, bashfulness, blankness, breadth, chill, chilliness, coldness, compass, constraint, coolness, detach, detachment, difference, disassociate, discreetness, discretion, dissemblance, dissimilitude, dissociate, distinction, divergence, divergency, expansion, expressionlessness,
extension, extent, field, footage, footing, frigidity, frostiness, gap, get ahead of, ground, guardedness, haughtiness, hauteur, hinterland, hold the field,
iciness, impassiveness, impassivity, impersonality, inaccessibility,
infinity, interval, introversion, leave behind,
length, lengthiness, linear
measures, locale, long
time, longitude,
longness, measure, mileage, mise-en-scene, modesty, offishness, orbit, otherness, outdistance, outpace, outrun, overall length, overpass, pass, perpetuity, perspective, piece, post, purview, radius, range, reach, rear, remoteness, repression, reserve, reservedness, restraint, reticence, reticency, retirement, rigidity, scene, scope, seat, separate, setting, shoot ahead of,
size, space, span, spell, spread, stage, stage set, stage setting,
stand, standing, standoffishness,
station, status, steal a march, stiffness, stretch, subduedness, suppression, surpass, sweep, theater, unaffability, unapproachability,
uncongeniality,
undemonstrativeness,
unexpansiveness,
unlikeness, venue, viewpoint, way, ways, withdrawal, withdrawnness, yardage