From Wikipedia, the free encyclopedia
This article is about distance in mathematics or physics.
For other uses, see .
Distance is a numerical description of how far apart objects are. In
or everyday usage, distance may refer to a physical length, or an estimation based on other criteria (e.g. "two counties over"). In , a distance function or
is a generalization of the concept of physical distance. A metric is a function that behaves according to a specific set of rules, and is a concrete way of describing what it means for elements of some space to be "close to" or "far away from" each other. In most cases, "distance from A to B" is interchangeable with "distance between B and A".
In , the distance between two points of the
can be found using the distance formula. The distance between (x1, y1) and (x2, y2) is given by:
Similarly, given points (x1, y1, z1) and (x2, y2, z2) in , the distance between them is:
These formula are easily derived by constructing a right triangle with a leg on the
of another (with the other leg
that contains the 1st triangle) and applying the . In the study of complicated geometries,we call this (most common) type of distance ,as it is derived from the ,which does not hold in .This distance
can also be expanded into the .
Rn, the distance between two points is usually given by the
(2-norm distance). Other distances, based on other , are sometimes used instead.
For a point (x1, x2, ...,xn) and a point (y1, y2, ...,yn), the
of order p (p-norm distance) is defined as:
1-norm distance
2-norm distance
p-norm distance
infinity norm distance
p need not be an integer, but it cannot be less than 1, because otherwise the
does not hold.
The 2-norm distance is the , a generalization of the
to more than two . It is what would be obtained if the distance between two points were measured with a : the "intuitive" idea of distance.
The 1-norm distance is more colourfully called the taxicab norm or , 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 . In 2D, it is the minimum number of moves
require to travel between two squares on a .
The p-norm is rarely used for values of p other than 1, 2, and infinity, but see .
In physical space the Euclidean distance is in a way the most natural one, because in this case the length of a
does not change with .
The Euclidean distance between two points in space ( and ) may be written in a
form where the distance is the minimum value of an integral:
is the trajectory (path) between the two points. The value of the integral (D) represents the length of this trajectory. The distance is the minimal value of this integral and is obtained when
is the optimal trajectory. In the familiar Euclidean case (the above integral) this optimal trajectory is simply a straight line. It is well known that the shortest path between two points is a straight line. Straight lines can formally be obtained by solving the
for the above . In
manifolds (curved spaces) where the nature of the space is represented by a
the integrand has be to modified to , where
has been used.
The Euclidean distance between two objects may also be generalized to the case where the objects are no longer points but are higher-dimensional , such as space curves, so in addition to talking about distance between two points one can discuss concepts of distance between two strings. Since the new objects that are dealt with are extended objects (not points anymore) additional concepts such as non-extensibility,
constraints, and non-local interactions that enforce non-crossing become central to the notion of distance. The distance between the two manifolds is the
that results from minimizing the generalized distance functional, which represents a transformation between the two manifolds:
The above double integral is the generalized distance functional between two plymer conformation.
is a spatial parameter and
is pseudo-time. This means that
is the polymer/string conformation at time
and is parameterized along the string length by . Similarly
is the trajectory of an infinitesimal segment of the string during transformation of the entire string from conformation
to conformation . The term with cofactor
and its role is to ensure that the length of the polymer remains the same during the transformation. If two discrete polymers are inextensible, then the minimal-distance transformation between them no longer involves purely straight-line motion, even on a Euclidean metric. There is a potential application of such generalized distance to the problem of
This generalized distance is analogous to the
in , however there is no exact correspondence because the Euclidean distance in 3-space is inequivalent to the space-time distance minimized for the classical relativistic string.
This section requires . (December 2008)
This is a metric often used in
that can be minimized by
estimation.
For curves or surfaces given by the equation
(such as a ), the algebraic distance from the point
to the curve is simply . It may serve as an "initial guess" for
to refine estimations of the curve by more accurate methods, such as .
In , in particular , a
on a given
d: M × M → R, where R denotes the set of , that satisfies the following conditions:
d(x,y) ≥ 0, and d(x,y) = 0
x = y. (Distance is positive between two different points, and is zero precisely from a point to itself.)
It is : d(x,y) = d(y,x). (The distance between x and y is the same in either direction.)
It satisfies the : d(x,z) ≤ d(x,y) + d(y,z). (The distance between two points is the shortest distance along any path). Such a distance function is known as a . Together with the set, it makes up a .
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
of the . 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 ""; with this definition numbers cannot be arbitrarily close.
d(A, B) & d(A, C) + d(C, B)
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 , 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
of a given set:
One version of distance between two non-empty sets is the
of the distances between any two of their respective points, which is the every-day meaning of the word, i.e.
This is a symmetric . 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 , i.e., the
does not hold, except in special cases. Therefore only in special cases this distance makes a collection of sets a .
is the larger of two values, one being the , 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
subsets of a metric space itself a .
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.
between two vertices is the length of the shortest
between those vertices.
Distance along a path compared with displacement
Distance cannot be
and distance travelled never decreases. Distance is a
quantity or a , whereas
quantity with both magnitude and . Directed distance is a positive, zero, or negative scalar quantity.
The distance covered by a vehicle (for example as recorded by an ), person, animal, or object along a curved path from a point A to a point B should be distinguished from the straight line distance from A to B. For example whatever the distance covered during a round trip from A to B and back to A, the displacement is zero as start and end points coincide. In general the straight line distance does not equal distance travelled, except for journeys in a straight line.
Directed distances are distances with a directional sense. They can be determined along straight lines and along curved lines. A directed distance of a point C from point A in the direction of B on a line AB in a
is the distance from A to C if C falls on the ray AB, but is the negative of that distance if C falls on the ray BA (I.e., if C is not on the same side of A as B is).
A directed distance along a curved line is not a vector and is represented by a segment of that curved line defined by endpoints A and B, with some specific information indicating the sense (or direction) of an ideal or real motion from one endpoint of the segment to the other (see figure). For instance, just labelling the two endpoints as A and B can indicate the sense, if the ordered sequence (A, B) is assumed, which implies that A is the starting point.
A displacement (see above) is a special kind of directed distance defined in . A directed distance is called displacement when it is the distance along a straight line (minimum distance) from A and B, and when A and B are positions occupied by the same particle at two different instants of time. This implies
of the particle. The distance traveled by a particle must always be greater than or equal to its displacement, with equality occurring only when the particle moves along a straight path.
Another kind of directed distance is that between two different particles or point masses at a given time. For instance, the distance from the
of the Earth A and the
of the Moon B (which does not strictly imply motion from A to B) falls into this category.
, or energy statistics, which are functions of distances between statistical observations
and , which are used in
, which measures the difference between two probability distributions
is used in
Circular distance is the distance traveled by a wheel. The circumference of the wheel is 2π × radius, and assuming the radius to be 1, then each revolution of the wheel is equivalent of the distance 2π radians. In engineering ω = 2π? is often used, where ? is the frequency.
Wikiquote has quotations related to:
– physical distance between people
SS Plotkin, PNAS.: 1,
AR Mohazab, SS Plotkin,"Minimal Folding Pathways for Coarse-Grained Biopolymer Fragments" Biophysical Journal, Volume 95, Issue 12, Pages
(2006), Dictionary of Distances, Elsevier,  .
: Hidden categories:cover the distance from……to……in……←(这里填什么)by……_百度作业帮
拍照搜题，秒出答案
cover the distance from……to……in……←(这里填什么)by……
cover the distance from……to……in……←(这里填什么)by……
from A to B in xxxx time.
时间段 in 3 hours 在三个小时之内乘坐什么工具 完成了多少距离第三人称单数:
distance是什么意思，词典释义与在线翻译：
距离，路程，间距
远处，远方
疏远，冷淡，隔阂
远隔，远离
长远，遥远，长久，久远
adj.(形容词)
远程（教育）的
使疏远，使远离
把…远远甩在后面，超过，赶过，胜过
隔开，把...放在一定距离之外，放在远处
与…疏远，与 ... 保持距离
比…做得更好或更多
使显得遥远，使显得有距离
[C][U]距离,间距 amount of space between two points or places
[C][U]远处,远方 distant place or point
[U](时间或空间的)相距 being separated in space or by time
[U]疏远,冷淡 social separation or coldness in personal relations
提示：各行业词典APP中含有本词条的独家正版内容，在手机上可看到更多释义内容。
distances&:&距离 ...
在&&中查看更多...
distances&:&距离 ...
在&&中查看更多...
distances&:&距离 ...
在&&中查看更多...
distances&:&距离, 差距 ...
在&&中查看更多...
distances&:&距离, 间距 ...
在&&中查看更多...
distances&:&距离, 差距 ...
在&&中查看更多...
the property created by the space between two objects or points
"I could see it in the distance"
size of the ga
"the distance from New York to Chicago"
"he determined the length of the shortest line segment joining the two points"
indifference by
"emotional distance"
the interv
"the distance from birth to death"
"it all happened in the space of 10 minutes"
"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"
"we have to distance ourselves from these events in order to continue living"
"He outdistanced the other runners"
distance的用法和样例：
用作名词 (n.)
He judged the distance to a nicety.
他判断距离很正确。
My house is four miles distance from the sea.
我家离海四英里。
We can see a windmill in the distance.
我们可以望见远处有架风车。
A lighthouse was winking in the far distance.
一座灯塔正在远处闪烁。
用作及物动词 (vt.)
A more appropriate stance would be for the leader to distance itself from the com-petitors.
作为领导者，一个较正确的姿态是在自己和对手之间，拉开距离 。
Interestingly, there are several reasons why it is so important to distance oneself from the rest.
有趣的是,一定要拉开和其他人的距离,背后有很多原因。
用作名词 (n.)
Walk on a short distance and there you are.
再往前走不了多远,你就到了。
It takes strength and attention to drive a truck long distances.
跑长途的汽车司机需要付出劳力,思想也要高度集中。
This is the point, from which all distances are measured.
从这一点开始来测量各方面的距离。
Our destination is still some distance away .
我们的目的地离这里还有一段路程。
The station is a good distance off.
车站离这儿很远。
It's some distance to the shopping centre.
到购物中心相当远。
It's no distance to the post office at all.
到邮局很近。
We have quite a distance to walk.
我们要走相当远的路程。
I was born in a town quite a distance from here.
我出生在离这儿很远的镇上。
In England and America distance is measured in miles, not in kilometres.
在英美,测量距离用英里作单位,不用公里。
Keep a safe distance between cars.
车与车之间要保持安全的距离。
You can see the mountains in the distance.
你可以看见远处的山。
I spotted something dark in the distance.
我望见远方有个黑黑的东西。
We heard gunfire in the distance.
我们听到远处的枪声。
A ship could be seen in the distance.
远处可以看到一艘船。
Look ahead in the distance, you can just see the lights of the village.
你若向前方远处看,你就能看见村里的灯光。
The balloon still can be seen in the distance.
这个大气球在远处仍能看见。
In the distance loomed a towering mountain.
在远处一座巍峨的高山隐约可见。
I live a short distance from school.
我家离学校不远。
We can see the mountain from a distance.
我们从远处就可以望见重重山峦。
The picture looks better from a distance.
从远处看,这幅画显得更好看一些。
From a distance the child heard a woman's scream.
从很远的距离这孩子就听见了女人的尖叫声。
Oil paintings are to be appreciated at a distance.
油画要在一定的距离外欣赏。
Your dress looks all right at a distance.
你的衣服远看不错。
The radar system can detect other planes at great distances and send a variety of radar-guided missiles to destroy them.
雷达能够探测出离它很远的飞机,并发射出各种由雷达制导的导弹把飞机摧毁掉。
He won't hit the target at that distance.
他打不中那样远的目标。
We planted the trees at a certain distance from each other.
我们植树时,株与株之间留出一定的间隔。
We can see the mountain at a distance of three kilometres.
我们在3公里处看到了那座山。
What is the distance between these two cities?
这两个城市相距有多远?
The living quarters for the workers are within walking distance of the factory.
工人住宅区离工厂很近,步行可以走到。
My house is within walking distance of the school.
我的房子和学校在步行可及的距离内。
There are three supermarkets within walking distance in this town.
这个镇上有三个超市,很近,步行就可到达。
The school is in easy walking distance.
学校很近,步行就可到达。
There was some distance between them at their last meeting.
他们上次见面彼此就有些疏远了。
They have always kept their distance from the neighbours.
他们很少接近左邻右舍。
We haven't heard from him at this distance of time.
在这样长的时间里,我们还没有接到他的信。
At this distance of time,I can't guarantee that I haven't omitted anything in recounting the event.
由于年代久远,我不能保证追述这个事件中没有任何遗漏。
Things look different at a distance of 10 years.
时隔10年,情况不同了。
用作名词 (n.)
go the distance
继续跑完全程,赛足全局等 continue to run, fight, etc. until the end of a contest
Even though the race course was in very bad conditions, all the horses went the distance.
尽管赛马场的跑道很糟糕,所有的马都跑完了全程。
Nobody thought he'd last 15 rounds, but he went the full distance.
没有人认为他会坚持15个回合,然而他终于打满了全局。
You need perseverance to win in politics and I doubt if he can go the distance.
在政治上,需要坚定不移才能取胜,我怀疑他能否坚持到底。
keep at a distance
与某人保持一段距离 refuse to let sb become familiar or friendly
keep sb at a distance
It was difficult to get to know her because she always kept everyone at a distance.要了解她很难,她老是对每个人都保持一段距离。
The captain kept his crew at a distance.船长对他的船员保持疏远。
keep one's distance (from)
与…保持一定的距离 not get too close to sb/sth
They were careful to keep their distance from the ill-tempered professor.
他们都谨慎地避开这位坏脾气的教授。
Keep your distance, or I'll shoot!
别靠近,否则就开枪了。
对(人或事业)等冷淡 not become friendly or familiar with (a person, cause, etc.)
He was asked many times to join the party, but he always kept his distance.
人家好几次要他参加那个政党,但他的反应总是很冷淡。
用作名词 (n.)
计算出距离
缩小…间的差距
穿过一段距离,横跨一段距离
徒步走这段距离
走完全程,经过全过程
不亲密,保持疏远
与某人保持相当距离,对某人疏远,敬而远之
跑一段距离
步行一段距离
计算出距离
一定的距离
交通方便的路程
相当远的距离
短距离,不远
听得见喊声的距离
走不多远就可达到的距离
遥远的路途
有相当距离,不很近
在一定距离
在如此长久的时间
成功指日可待
之间的距离
纽约和伦敦之间的距离
两个物体间的距离
贫富间的悬殊
从东到西的距离
五公里之遥
太阳到地球间的距离
Afar the Contadino's song is heard..made sweet by distance.
出自：Shelley
A bench some distance from the bed.
出自：C. H. Sisson
The friendly Sea conveniently distanced from London.
出自：T. Fuller
She had..interests outside his range, interests which..distanced her from him.
出自：L. P. Hartley
distance的详细讲解：
distance的基本意思是表示空间的“距离”“间距”,也可表示“远处”“远方”,可用作可数名词,也可用作不可数名词。distance还可用来表达时间。表示“(时间或空间的)相距”时,是不可数名词。
distance前可加冠词,有great, enormous, all, long等定语修饰时,常用复数形式distances。
in the distance指“在远方,远方的”,表示耳、目所及的地方。some distance, a good distance, quite a distance和a great distance都表示“相当远”“很长一段时间”“有相当一段距离”。in〔within〕 (easy) walking distance表示“在步行可到达的范围之内”。
distance用于比喻可表示“冷淡”“疏远”,是不可数名词。
distance用作动词表示“使某人与某人保持距离”“使某人与某人关系疏远或冷淡”“与某人〔某事物〕保持距离”。例如:That stupid quarrel has distanced us.那一场无谓的争吵使我们的关系疏远了。Voters have been distanced from the party by adverse publicity.选民受到反面宣传的影响,对这个政党冷淡了。She needs to distance herself from some of her more extreme supporters.她必须与拥护她的那些比较偏激的人保持一定的距离。
at the distance, from the distance, in the distance
1.at a distance表示在有一定距离的远处; in the distance则是“在远处”的意思; from a distance表示“从远处”。
2.in the distance偶尔还可作定语。
☆ 13世纪晚期进入英语，直接源自古法语的destance；最初源自古典拉丁语的distantia：dis （分开） + staia (站），意为分开站。
distance的海词问答与网友补充：
distance的相关资料：
distances&:&距离，间距 ...
在&&中查看更多...
distances&:&距离 ...
在&&中查看更多...
distances&:&距离；路程 ...
在&&中查看更多...
【近义词】
宽阔的区域
在 ... 中间
在 ... 之间
distances:distance n. 距离, 远离, 一长段时间, 远方, 远景, 遥远, (时间的)间隔, (时日的)经过 英英解释:名词distance:1. the property created by t…
相关词典网站：}