Distance 中文

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曼哈頓距離[编辑]
在棋盤上的距離計量[编辑]
參見[编辑]
參考資料[编辑]
外部連結[编辑]

曼哈頓與歐幾里得距離：紅、藍與黃線分別表示所有曼哈頓距離都擁有一樣長度（12），而綠線表示歐幾里得距離有6×√2 ≈ 8.48的長度。

計程車幾何（Taxicab geometry）或曼哈頓距離（英語：Manhattan distance/Manhattan length）或方格線距離是由十九世紀的赫尔曼·闵可夫斯基所創辭彙，為歐幾里得幾何度量空間的幾何學之用語，用以標明兩個點上在標準坐標系上的絕對軸距之總和。

曼哈頓距離[编辑]

我們可以定義曼哈頓距離的正式意義為L1-距離或城市區塊距離，也就是在欧几里得空间的固定直角坐标系上兩點所形成的线段對軸產生的投影的距離總和。

例如在平面上，坐標（x1, y1）的點P1與坐標（x2, y2）的點P2的曼哈頓距離為：

要注意的是，曼哈頓距離依賴座標系統的旋轉，而非系統在座標軸上的平移或映射。

曼哈頓距離的命名原因是從規劃為方型建築區塊的城市（如曼哈頓）間，最短的行車路徑而來（忽略曼哈頓的單向車道以及只存在於3、14大道的斜向車道）。任何往東三區塊、往北六區塊的的路徑一定最少要走九區塊，沒有其他捷徑。

計程車幾何學滿足除了SAS全等定理之外的希尔伯特几何公理。

在計程車幾何學中，一個圓是由從圓心向各個固定曼哈頓距離標示出來的點圍成的區域，因此這種圓其實就是旋轉了45度的正方形。如果有一群圓，且任兩圓皆相交，則整群圓必在某點相交；因此曼哈頓距離會形成一個超凸度量空間。對一個半徑為r 的圓來說，這個正方形的圓每邊長√2r。此'"圓"的半徑r對切比雪夫距離（L∞空間）的二維平面來說，也是一個對座標軸來說邊長為2r的正方形，因此二維切比雪夫距離可視為等同於旋轉且放大過的二維曼哈頓距離。然而這種介於L1與L∞的相等關係並不能延伸到更高的維度。

在棋盤上的距離計量[编辑]

在西洋棋裡，車（城堡）是以曼哈頓距離來計算棋盤格上的距離；而王（國王）與后（皇后）使用切比雪夫距離，象（主教）則是用轉了45度的曼哈頓距離來算（在同色的格子上），也就是說它以斜線為行走路徑。只有國王需要一步一步走的方式移動，皇后、主教與城堡可以在一或兩次移動走到任何一格（在沒有阻礙物的情況下，且主教忽略它不能走到的另一類顏色）。

參見[编辑]

距離
切比雪夫距离
赋范向量空间
度量
正交凸包
汉明距离

參考資料[编辑]

Eugene F. Krause. Taxicab Geometry. Dover. 1987. ISBN 978-0-486-25202-5.

外部連結[编辑]

City Block Distance （页面存档备份，存于互联网档案馆），by Kardi Teknomo
city-block metric （页面存档备份，存于互联网档案馆） on PlanetMath
埃里克·韦斯坦因. Taxicab Metric. MathWorld.
Manhattan distance （页面存档备份，存于互联网档案馆）。Paul E. Black, Dictionary of Algorithms and Data Structures （页面存档备份，存于互联网档案馆），NIST

The Organization has also

[...] provided supportfor distancetrainingforall participating [...]

libraries and for the coordination

[...]

of the virtual working group for the project.

unesdoc.unesco.org

本组织还为所有参加该项目的图书馆的远程培训，为该项目虚拟工作组的协调提供了支助。

unesdoc.unesco.org

Besides, most schools in Hong Kong organize other jogging-related activities annually, such as distance-running

[...] [...] competitions, round-the-campus runs and cross-country races, and include competition eventsfor distancerunning in their annual athletic meets.

legco.gov.hk

大部分學校每年更會舉辦其他緩跑活動，如長跑比賽、環校跑或越野跑，並於陸運會中加入長跑競賽項目。

legco.gov.hk

In the future, developing countries may be able to build a national digital network to provide access to library resources from around the world to every remote village, as is being done in Australia.28 Similarly, initiatives such as the African Virtual

[...]

University (AVU) are showing the potential of the Internet as a tool

[...] and resourcefor distance learning in the [...]

developing world.

iprcommission.org

28 同样，诸如建立“非洲虚拟大学”(AVU) 之类的动议显示出因特网在发展中国家作为远程教学工具和资源的潜能。

iprcommission.org

Select units of measurefor distanceand speed, direction, [...]

elevation, and temperature.

garminasus.com

選取距離及速度、方向、高度及溫度的測量單位。

garminasus.com

ITU launched a network of Centres of Excellence in African countries to

[...]

promote the use of information and communications technology

[...] in educationfor distancelearning and [...]

face-to-face training.

daccess-ods.un.org

国际电信联盟在非洲国家建立了英才中心网络，推动在教育领域使用信息和通信技术，进行远距离学习和面对面培训。

daccess-ods.un.org

Configure 4 (Screen

[...] 21) allows users to set preferred unitsfor distance,volume, and pressure.

gww.graco.com

配置 4 （屏幕 21）可使用户设置喜欢的长度和体积单位。

gww.graco.com

In addition to the above subjects, UNESCO Jakarta Office also dealt with other important issues in the field of communication and information, such as widening people’s access to communication and information through the establishment of Community Multimedia Centres in

[...]

Indonesia as well as in

[...] Timor-Leste, creating online sourcesfor distance learning, and promoting media literacy [...]

for youth.

unesdoc.unesco.org

除了上述主题，教科文

[...] 组织雅加达办事处还处理了在通讯和信息领域的其他重要问题，比如通过在印度尼西亚和东帝汶成立社区多媒体中心、在互联网上创建远程学习的资源，以及促进对青年的媒体扫盲扩大人们获得通讯和信息的机会。

unesdoc.unesco.org

Configure

[...] 4 (Screen 21) controls unitsfor distanceand volume.

gww.graco.com

配置 4 （屏幕 21）控制长度及体积单位。

gww.graco.com

However, in recent years, the educational sector has played an

[...] [...] increasingly active role, calling for amendments to the law to address electronic copyright and to make provisionfor distanceeducation, special educational programmes and the needs of disabled people (for example, the blind).

iprcommission.org

但在近些年来，教育部门起到越来越多的积极作用，呼吁修改立法，强调电子著作权，要求为远程教育、特殊教育项目和残疾人（如盲人）教育需求等制定相关规定。

iprcommission.org

Adjustable gain control - automatically and manually adjusts

[...] signal strength to compensatefor distance

aten.co.uk

視訊增益控制功能，可依距離遠近以自動與手動方式補強視訊訊號強度

aten.com.tw

Gently advance the monofilament suture from the lumen of the ECA

[...] into the ICAforadistanceof 9-10 mm beyond [...]

the bifurcation of CCA to occlude the origin of MCA.

jove.com

轻轻提前进入ICA单丝缝合了9-10毫米以外的CCA分叉处闭塞马华起源的距离，从非洲经委会流明。

jove.com

The Special Rapporteur then highlights some of the good practices he was able to observe during his visit, such as the high enrolment rates and how Mongol society values education; and other examples such as the mobile ger kindergartens and school snacks, as well as some

[...]

programmes of education for minorities

[...] and incentivesfor distance education that [...]

show creativity and adaptation to the

[...]

vastness of the land and the climatic conditions encountered.

daccess-ods.un.org

特别报告员然后着重谈到他在访问期间所看到的若干良好做法，如入学率高和蒙古社会如何重视教

[...] 育；其他的例子如：流动蒙古包幼儿园和校餐、以及针对少数民族的一些教育方案和远程教育刺激办法，这些做法富有创意，适于该国土地辽阔的状况和气候条件。

daccess-ods.un.org

No matter it is a sports game, commencement, school summit,

[...]

student play, or musical performance, there are always some people missing the

[...] glory momentsfor distance,time or weather.

solutions.avermedia.com

無論是運動賽事、畢業典禮、校園研討會、學生話劇或音樂會，總會 有人因 為距離、時間或天氣而無法親臨現場。

solutions.avermedia.com

(c) Funding from donors will be maintained and/or obtained for the revision and fielding of the “Security Awareness for United Nations Personnel” and “Advanced Security in the

[...]

Field” learning programmes and for the fielding and maintenance of the

[...] learning management systemfor distance learning

daccess-ods.un.org

CE-252 features two gain control modes for an excellent video transmission (1600x1200 resolutions, DDC2B): the Automatic Gain Control function automatically identifies the distance which needs to be bridged and optimizes the signal

[...]

strength, and the Adjustable Gain Control allows users to manually adjust the

[...] signal strength to compensatefor distance.

pl.aten.eu

CE-252為達到優越的視訊品質(解析度1600x1200,

[...] DDC2B)，提供了二種不同的視訊訊號增益控制方式，一種是自動增益控制功能，可自動偵測連線距離以將訊號強度調整至最佳模式；另一種則是可調式增益控制功能，使用者可以依延長距離手動調整訊號強度。

aten.com.tw

Watch outfor distanceand wind factors [...]

that will affect your shot.

flashghetto.be

警惕的距離和風力因素會影響您的鏡頭。

flashghetto.tw

Several pilot projects

[...] implemented in 2009 aimed at enhancing opportunitiesfor distancelearning, vocational training and community technology access.

daccess-ods.un.org

2009 年实施了若干旨在加强函授、职业培训和社区技术获得机遇的试点性项目。

daccess-ods.un.org

In using the instrumentfor distancemeasurements orforpositioning moving objects (e.g. cranes, building equipment, platforms, etc.) unforeseen [...] [...]

events may cause erroneous measurements.

stabila.de

在测量或定位一个动态目标时（如：吊车，建筑机械或平台），可能会因意外情况而造成错误测量结果。

stabila.de

Request further product documentation or pricesfor Distanceholders from Treckerteile 24 GmbH.

industrystock.com

关于更多间隔区的服务或附件信息，请联系企业Treckerteile 24 GmbH。

industrystock.cn

The minimum value must be used for measurements at right angles to

[...] the target; the maximumdistance forall other measurements.

leica-geosystems.be

最小值测量功能可以用在直角边测量中，而最大值测量则用在其他边的测量上。

leica-geosystems.be

The areas where native title was

[...]

found were in the intertidal zones and

[...] adjoining seasforadistanceof 5 nautical [...]

miles offshore from the islands which

[...]

had been inhabited at sovereignty, 0.5 nautical miles around other islands uninhabited at sovereignty, and a distance ranging from 2.7-5 nautical miles off the mainland coast.

daccess-ods.un.org

认为具有土著产权的地区位于潮间带和毗连海域，这块地方距离具有主权、有人居住的岛屿海岸 5 海里，距离具有主权、无 [...]

人居住的其他岛屿 0.5 海里，距离大陆海岸 2.7-5 海里。

daccess-ods.un.org

Though some experts made the point that the notion of “cultural goods and services” evokes the vocabulary used in agreements on international trade, the Group felt that the proposed definition boiled down to a

[...]

more cultural conception of this notion,

[...] thus allowingforadistancingfrom the strictly [...]

trade-related understanding, while

[...]

recognizing the dual nature of these goods and services.

unesdoc.unesco.org

尽管专家中有些人提出要注意“文化产品和服务”的概念有可能使

[...] 人想到在国际贸易协定中所使用的这一用语内涵的问题，它们最终还是认 为他们 提出的定义能使人们的理解回到这一概念的文化内涵，从而摆脱其纯商业性的意义并达成对这些产品和 [...]

服务的双重禀赋的认可。

unesdoc.unesco.org

Plug and play interconnection using

[...]

a USB Cable (Universal Serial Bus)

[...] is recommendedforwiringdistancesup to 16.4 feet [...]

(5 meters) between the Transceiver and Matrix PC.

graco.com

推荐将配有 USB 电缆（通用串行总线）的即插即用

[...] 互连电缆用于收发器和 Matrix 电脑之间的布线距离最长达 16.4 英尺（5 米）的连接。

graco.com

Road curvature is in accordance with highway design standards with regard to

[...] geometric valuesforradii and sightdistancesrequirements.

devb.gov.hk

道路的彎度是按照道路設計標準中有關半徑的幾何值和視線距離要求來確定的。

devb.gov.hk

For horizontal coupling plate and

[...]

vertical coupling plate

[...] discharge, there is a certaindistance forthe coupling plate from [...]

the equipment, and through two

[...]

pieces of 470k ohm resistors to ground, so when the coupling plate discharge, the electrostatic of coupling board will not immediately release into the ground, but to form an electrostatic field sourced by coupling plate and interfere to equipment.

sfi.com.tw

對水平耦合板和垂直耦合板進行放電，耦合板距離設備有一定距離，並通過兩個470k歐姆的電阻接地，所以當對耦合板放電時，耦合板上的靜電不會馬上洩放到地，而以耦合板為靜電源形成一靜電場，對設備進行干擾。

sfi.com.tw

Two of the 4 general temporary assistance positions, 1 P-4 and 1 P-3 Training Officers, and 1 P-4 continuing post, currently funded from the support account, design, deliver, upgrade, harmonize and evaluate three ongoing cross-cutting leadership programmes: the senior mission leaders’ programme, a two-week course, conducted twice annually at a host Member State, for 26 candidates from Member States, the Secretariat, the United Nations agencies, programmes and funds); the senior leaders’ programme, a compulsory orientation course for all mission personnel at the D-2 level and above, conducted twice annually in New York; and SMART, an

[...]

intensive year-long

[...] programme involvingdistancelearning and three week-long workshopsfortwo groups of [...]

40 candidates.

daccess-ods.un.org

4 个一般临时人员职位中的 2 个，即 1 个 P-4 和 1 个 P-3 培训干事，以及 1 个 P-4 续设员额，目前由支助账户供资，负责设计、提供、升级、统一和评价目前三个贯穿各领域的领导方案：高级特派团领导方案为期 2 个星期的课程，每年由一个会员国主办两次，每次有来自会员国、秘书处以及联合国机构、方案

[...]

和基金的 26 名候选人参加；高级领导方案是特派团所有 D-2 及以上级别的人员

[...] 必须参加的概况介绍课程，每年在纽约举行两次；高级行政管理和资源培训方案为两组 40 名候选人提供的持续一年的强化方案，包含远程教学和为期三个星期的讲习班。

daccess-ods.un.org

Under the Outcome on strengthened national capacity in extending affordable and effective health and

[...] [...] education services, UNESCO has indicated its readiness to support efforts to improve the quality of education through curriculum revision, pre-service and in-service teacher training, and in expanding the quality and reach of e-baseddistance learning teacher training programmes, particularly targetedforteachers in the outer islands.

unesdoc.unesco.org

根据关于加强提供可支付得起的和有效的保健和教育服务国家能力的成果，教科文组织已经表明愿意通过修订教学大纲、任职前和在职教师培训支助改善教育质量的努力，并提高网络在线教师培训方案的质量和覆盖面，特别是针对在外侧的岛的教师。

unesdoc.unesco.org

Some of the

[...] elements of a visionforalowcarbon transport system could include: (a) dense, but green, and mixed-use cities that provide jobs, and shopping and leisure facilities close to people’s residential areas; (b) modern, high-quality links between the centres and good integration of long-distance hubs with local [...]

transportation; (c)

[...]

high-quality alternatives to individual car use, in particular efficient public transport and good non-motorized transport infrastructure and its proper integration; (d) efficient, intermodal freight transport and smart urban logistics that also include clean vehicles; and (e) advanced technologies such as hybrid engines, alternative fuels or even electric motorbikes and cars.

daccess-ods.un.org

低碳交通系统愿景的一些要素可以包括：(a) 密集但绿色、混合用途城市，在居民区附近提供就业及购物和休闲设施；(b) 中心区之间现代化高质量连接，长途枢纽与当地交通融为一体；(c) 个人汽车使用的高质量替代，特别是高效率的公共交通、良好的非机动化交通基础设施及其适当的一体化：(d) 高效率的多式货物联运和智能城市物流，其中包括清洁车辆；以及(e) 混合动力引擎、代用燃料、甚至电动摩托车和汽车等先进技术。

daccess-ods.un.org