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List of largest cities
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Population tables
of world cities
World's largest cities
World's largest cities proper
World's largest conurbations
World's largest urban areas
World megacities
World megalopolises
v
t
e
Determining the world's largest cities depends on which definitions of city are used. The United Nations uses three definitions for what constitutes a city, as not all cities may be classified using the same criteria.[1] Cities may be defined as the cities proper, the extent of their urban area, or their metropolitan regions.[1]
Contents
1 Common methods for defining the boundaries of a city
1.1 City proper (administrative)
1.2 Urban area
1.3 Metropolitan area
2 Largest cities
3 See also
4 Notes
5 References
6 External links
Common methods for defining the boundaries of a city[edit]
City proper (administrative)[edit]
For a more comprehensive list, see List of cities proper by population.
A city can be defined by its administrative boundaries (city proper). World Urbanization Prospects, a UN publication, defines population of a city proper as "the population living within the administrative boundaries of a city or controlled directly from the city by a single authority." UNICEF[1] defines city proper as "the population living within the administrative boundaries of a city, e.g., Washington, D.C.". A city proper is a locality defined according to legal or political boundaries and an administratively recognised urban status that is usually characterised by some form of local government.[2][3][4] Cities proper and their boundaries and population data may not include suburbs.[5]
The use of city proper as defined by administrative boundaries may not include suburban areas where an important proportion of the population working or studying in the city lives.[5] Because of this definition, the city proper population figure may differ greatly with the urban area population figure, as many cities are amalgamations of smaller cities (Australia), and conversely, many Chinese cities govern territories that extend well beyond the traditional "city proper" into suburban and rural areas.[6]
Urban area[edit]
For a more comprehensive list, see List of urban areas by population.
See also: Number of urban areas by country
A city can be defined as a conditionally contiguous urban area, without regard to territorial or other boundaries inside an urban area. UNICEF[1] defines urban area as follows:
The definition of "urban" varies from country to country, and, with periodic reclassification, can also vary within one country over time, making direct comparisons difficult. An urban area can be defined by one or more of the following: administrative criteria or political boundaries (e.g., area within the jurisdiction of a municipality or town committee), a threshold population size (where the minimum for an urban settlement is typically in the region of 2,000 people, although this varies globally between 200 and 50,000), population density, economic function (e.g., where a significant majority of the population is not primarily engaged in agriculture, or where there is surplus employment) or the presence of urban characteristics (e.g., paved streets, electric lighting, sewerage).
Metropolitan area[edit]
For a more comprehensive list, see List of metropolitan areas by population.
A city can be defined by the habits of its demographic population, as by metropolitan area, labour market area, or similar in a metropolitan area. UNICEF[1] defines metropolitan area as follows:
A formal local government area comprising the urban area as a whole and its primary commuter areas, typically formed around a city with a large concentration of people (i.e., a population of at least 100,000). In addition to the city proper, a metropolitan area includes both the surrounding territory with urban levels of residential density and some additional lower-density areas that are adjacent to and linked to the city (e.g., through frequent transport, road linkages or commuting facilities).
Largest cities[edit]
City
Nation
Image
Population
City proper
Metropolitan area
Urban area[7]
Chongqing
China 30,165,500[8] 8,189,800[a]
Shanghai
China 24,256,800[10] 24,750,000[11] 23,416,000[b]
Delhi
India 21,678,794[12] 21,753,486[13]
Beijing
China 21,516,000[14] 24,900,000[15] 21,009,000
Mumbai
India 21,247,844[13] 21,771,200 22,748,395[13]
Dhaka
Bangladesh 19,840,000[16] 19,580,000[17][18]
Lagos
Nigeria 16,060,303[c] 21,000,000[21] 13,123,000
Chengdu
China 16,044,700[22] 10,376,000
Karachi
Pakistan 14,910,352[23][d]
Guangzhou
China 14,043,500[27] 44,259,000[28] 20,800,654[29]
Istanbul
Turkey 14,025,000[30] 13,520,000 14,657,000[30]
Tokyo
Japan 13,513,734[31] 37,843,000 36,923,000[32]
Tianjin
China 12,784,000 15,469,500 6,859,779[33]
Moscow
Russia 12,197,596[34] 16,170,000 16,800,000
São Paulo
Brazil 12,038,175[35] 21,090,791 36,842,102[36]
Lahore
Pakistan 11,126,285[37] 13,569,000 10,665,000[38]
Cairo
Egypt 10,230,350[39] 18,290,000 22,439,541
Seoul
Korea, South 10,197,604[40] 12,700,000 25,520,000[41]
Kinshasa
DR Congo 11,855,000[42] 13,265,000
Jakarta
Indonesia 10,075,310[43] 30,539,000 30,075,310[44]
Wenzhou
China 9,175,000[45] 9,122,102[45] 6,642,592
Mexico City
Mexico 8,974,724[46] 20,063,000 21,178,959[47]
Lima
Peru 8,852,000[48] 10,750,000 9,886,647[49]
London
United Kingdom 8,787,892[50] 13,879,757 9,787,426[51]
Xi'an
China 8,705,600[52] 13,569,700[53]
Bengaluru
India 8,692,500[13] 9,955,450[13]
Chennai
India 8,570,880[54] 9,373,521[13]
New York City
United States 8,537,673[55] 20,153,634[56] 23,689,255[57]
Hyderabad
India 8,425,970[13] 8,807,000 9,728,906[13]
Shenzhen
China 8,378,900[58][e] 12,084,000
Bangkok
Thailand 8,750,600[59] 15,931,300[60][better source needed] 15,645,000[61][better source needed]
Suzhou
China 8,265,050[62]
Nanjing
China 8,230,000[63] 34,360,000[64]
Dongguan
China 8,220,207[65][58][f]
Tehran
Iran 8,154,051[66] 13,532,000 14,595,904[67]
Quanzhou
China 8,128,533 6,107,475 1,435,185
Shenyang
China 8,106,171[55] 6,255,921
Bogotá
Colombia 7,878,783[68] 9,800,000[69][70] 9,520,000[7]
Ho Chi Minh City
Vietnam 8,426,100[71]
Hong Kong
China 7,274,900[72]
Baghdad
Iraq 7,180,889[73]
Fuzhou
China 7,115,369 4,468,076
Changsha
China 7,044,118[74]
Wuhan
China 6,886,253[75]
Hanoi
Vietnam 6,844,100[71]
Rio de Janeiro
Brazil 6,429,923[76] 12,727,000 13,973,505[35]
Qingdao
China 6,188,100 9,046,200 6,188,100
Foshan
China 6,151,622[77][78][58][g]
Zunyi
China 6,127,009
Santiago
Chile 5,743,719[79] 6,683,852[80]
Riyadh
Saudi Arabia 5,676,621[81]
Ahmedabad
India 5,570,585[13] 6,352,254[13]
Singapore
Singapore 5,535,000[82]
Shantou
China 5,391,028[83] 11,535,677
Ankara
Turkey 5,271,000[30] 4,585,000[30] 4,919,000[30]
Yangon
Myanmar 5,214,000[84]
Saint Petersburg
Russia 5,191,690[85] 5,900,000 6,200,000
Casablanca
Morocco 5,117,832[86] 6,861,739 6,861,739
Sydney
Australia 208,374[87] 5,029,768[88]
Abidjan
Ivory Coast 4,765,000[89]
Melbourne
Australia 135,959[90] 4,741,929[91]
Alexandria
Egypt 4,616,625[92]
Kolkata
India 4,486,679[13] 14,667,000 14,617,882[13]
Surat
India 4,462,002[13]
Johannesburg
South Africa 4,434,827[93]
Dar es Salaam
Tanzania 4,364,541[94]
Shijiazhuang
China 4,303,700 10,701,600 4,303,700
Harbin
China 4,280,701[95][96] 10,635,971 6,704,573
Giza
Egypt 4,239,988[97]
İzmir
Turkey 4,168,000[30] 3,019,000[30] 3,575,000[30]
Zhengzhou
China 4,122,087[98]
New Taipei City
Taiwan 3,954,929[99]
Los Angeles
United States 3,884,307[100] 15,058,000 13,262,220[101]
Changchun
China 3,815,270 7,674,439[102] 4,193,073
Cape Town
South Africa 3,740,026[93]
Yokohama
Japan 3,726,167[31][h]
Khartoum
Sudan 3,639,598 5,274,321 5,345,000[103]
Guayaquil
Ecuador 3,600,000[104] 5,000,000
Hangzhou
China 3,560,391[105]
Xiamen
China 3,531,347[106] 5,114,758 1,861,289
Berlin
Germany 3,517,424[107] 5,871,022
Busan
Korea, South 3,510,833[41] 8,202,239[108]
Ningbo
China 3,491,597[109] 7,639,000 3,491,597
Jeddah
Saudi Arabia 3,456,259[110]
Durban
South Africa 3,442,361[93]
Algiers
Algeria 3,415,811 5,000,000
Kabul
Afghanistan 3,414,100[111]
Hefei
China 3,352,076[112]
Mashhad
Iran 3,312,090 3,372,660
Pyongyang
Korea, North 3,255,388[113]
Madrid
Spain 3,207,247[114] 6,378,297[51]
Faisalabad
Pakistan 3,203,846[37]
Baku
Azerbaijan 3,202,300 4,308,740 3,525,000[115]
Tangshan
China 3,187,171 7,536,521 3,187,171
Ekurhuleni
South Africa 3,178,470[93]
Nairobi
Kenya 3,138,369[116]
Zhongshan
China 3,121,275[117]
Pune
India 3,115,431[13]
Addis Ababa
Ethiopia 3,103,673[118] 4,567,857 3,384,569
Jaipur
India 3,073,350[13]
Buenos Aires
Argentina 3,054,300[119] 14,122,000 13,074,000[120]
Incheon
Korea, South 2,978,367[121]
Quezon City
Philippines 2,936,116[122][i]
Toronto
Canada 2,929,886[123] 6,346,088[123] 6,129,900
Kiev
Ukraine 2,908,703[124] 3,375,000[125]
Salvador
Brazil 2,902,927[126] 3,919,864[127]
Rome
Italy 2,877,215[128] 4,353,775[129][j]
Dubai
United Arab Emirates 2,865,560[130]
Luanda
Angola 2,825,311 6,542,944[131]
Lucknow
India 2,815,601[13]
Kaohsiung
Taiwan 2,778,918[132] 2,540,000
Kanpur
India 2,768,057[133] 3,152,317 2,920,496[134]
Surabaya
Indonesia 2,765,487[135] 7,302,283 9,115,485[136][137]
Taichung
Taiwan 2,752,413[138] 2,520,000[139]
Basra
Iraq 2,750,000[140]
Taipei
Taiwan 2,704,974 7,045,488[141]
Chicago
United States 2,695,598[142] 9,156,000 9,554,598[101]
Osaka
Japan 2,691,742[31] 19,341,976[32] 17,444,000
Quito
Ecuador 2,671,191 4,700,000
Chaozhou
China 2,669,844
Fortaleza
Brazil 2,609,716 4,019,213
Chittagong
Bangladesh 2,581,643[143] 4,009,423
Bandung
Indonesia 2,575,478 6,965,655 8,495,928[136]
Managua
Nicaragua 2,560,789 2,205,676
Brasília
Brazil 2,556,149[144] 3,919,864[127]
Belo Horizonte
Brazil 2,502,557[145] 5,156,217
Daegu
Korea, South 2,492,994[146]
Houston
United States 2,489,558[147] 6,490,180 4,944,332
Douala
Cameroon 2,446,945[148]
Medellin
Colombia 2,441,123[149] 3,731,447 2,497,870
Yaoundé
Cameroon 2,440,462[148]
Nagpur
India 2,405,665[150] 2,497,870
Cali
Colombia 2,400,653[151] 3,400,000
Tashkent
Uzbekistan 2,309,600
Nagoya
Japan 2,296,014[31] 9,107,414[32] 10,177,000
Isfahan
Iran 2,243,249
Phnom Penh
Cambodia 2,234,566
Paris
France 2,229,621 12,405,426 10,601,122
Ouagadougou
Burkina Faso 2,200,000 2,500,000
Lanzhou
China 2,177,130 3,616,163 2,177,130
Kano
Nigeria 2,153,225 3,395,000 9,383,682
Dalian
China 2,146,099 5,935,638 3,964,593
Guatemala City
Guatemala 2,110,100[152] 4,500,000[152]
Havana
Cuba 2,106,146[153]
Rawalpindi
Pakistan 2,098,231[37]
Medan
Indonesia 2,097,610 4,103,696
Accra
Ghana 2,070,463[154] 4,010,054[154]
Visakhapatnam
India 2,035,922 5,340,000[155]
Gujranwala
Pakistan 2,027,001[37]
Jinan
China 2,009,273 5,853,196
Karaj
Iran 1,973,470
Peshawar
Pakistan 1,970,042[37]
Minsk
Belarus 1,959,781[156]
Caracas
Venezuela 1,943,901 2,923,959
Sana'a
Yemen 1,937,451[31] 2,167,961
Sapporo
Japan 1,918,096[31] 2,584,880
Tainan
Taiwan 1,885,252[157] 1,170,000[158]
Bucharest
Romania 1,883,425 2,272,163[159] 1,931,000[160]
Curitiba
Brazil 1,879,355 3,400,000
Shiraz
Iran 1,869,001
Vienna
Austria 1,863,881 2,600,000
Brazzaville
Congo Republic 1,827,000
Bhopal
India 1,798,218[161] 1,864,389 1,745,333
Almaty
Kazakhstan 1,792,549[162] 2,460,400[163]
Hamburg
Germany 1,787,408[164] 5,046,182
Manila
Philippines 1,780,148[122] 12,877,253[122] 24,123,000
Kuala Lumpur
Malaysia 1,768,000[165] 7,200,000[166]
Maputo
Mozambique 1,766,184 1,766,823
Budapest
Hungary 1,759,407[167] 2,927,944[168] 3,303,786
Warsaw
Poland 1,753,977[169] 3,100,844[168]
Lusaka
Zambia 1,742,979 2,467,467
Kathmandu
Nepal 1,744,240 2,517,023 3,207,205
Tabriz
Iran 1,733,033[170]
Hyderabad
Pakistan 1,732,693[37]
Palembang
Indonesia 1,708,413
Tijuana
Mexico 1,696,923 1,895,797
Patna
India 1,683,200 2,231,554 2,046,652[171]
Montreal
Canada 1,649,519 4,127,100 3,407,963
Davao City
Philippines 1,632,991[172] 2,516,216[k]
Harare
Zimbabwe 1,606,000 1,619,000[173]
Barcelona
Spain 1,604,555[174] 5,375,774 4,740,000[175]
Maracaibo
Venezuela 1,599,940[176] 3,897,655 2,658,355
Caloocan
Philippines 1,583,978[122][l]
Philadelphia
United States 1,567,872[177] 6,069,875[178] 7,183,479[179]
Novosibirsk
Russia 1,567,087[180]
Phoenix
United States 1,563,025[181] 4,574,531 3,629,114
Bulawayo
Zimbabwe 1,050,000 1,200,000[182]
Oran
Algeria 1,560,329[183] 3,454,078
Semarang
Indonesia 1,555,984 3,183,516
Recife
Brazil 1,555,039 3,743,854
Kobe
Japan 1,536,499[31][m]
Daejeon
Korea, South 1,535,028
Kampala
Uganda 1,507,080
Kawasaki
Japan 1,496,035[31][n]
Guadalajara
Mexico 1,495,189 4,424,252
Auckland
New Zealand 1,495,000[184] 1,614,300[185]
Vijayawada
India 1,491,202[186] 5,873,588
Fukuoka
Japan 1,483,052[31] 5,590,378
Kwangju
Korea, South 1,477,780[146]
Porto Alegre
Brazil 1,476,867 4,405,769
Kyoto
Japan 1,474,570[31][o]
San Antonio
United States 1,469,845[187] 2,454,061
Santa Cruz de la Sierra
Bolivia 1,453,549[citation needed] 1,749,000
Munich
Germany 1,450,381[188] 2,606,021
Kharkiv
Ukraine 1,449,414[189] 1,650,000[190]
Yekaterinburg
Russia 1,428,042
San Diego
United States 1,394,928[187] 3,095,313 2,956,746
Barranquilla
Colombia 1,386,865[191] 2,370,753[191]
Milan
Italy 1,359,905[192] 3,206,465[p]
Ibadan
Nigeria 1,338,659 2,837,000 3,375,000
Makassar
Indonesia 1,338,633 1,976,168
Córdoba
Argentina 1,330,023[193] 1,528,000
Prague
Czech Republic 1,324,000[194]
Mandalay
Myanmar 1,319,452[195] 1,726,889
Dallas
United States 1,317,929[196] 7,233,323[197] 5,121,892[198]
Montevideo
Uruguay 1,305,082[199] 1,947,604 1,719,453
Sofia
Bulgaria
1,260,120 1,682,340 1,547,472
Nizhny Novgorod
Russia 1,250,619[200]
Abuja
Nigeria 1,235,880 6,000,000[201] 2,440,000
Calgary
Canada 1,235,171[202] 1,214,839 1,095,404
Saitama
Japan 1,226,656[31][q]
Suwon
South Korea 1,202,310
Hiroshima
Japan 1,196,274
Rosario
Argentina 1,193,605[203] 1,276,000[204]
Brisbane
Australia 1,180,285[205] 2,360,241[206][207]
Belgrade
Serbia 1,166,763[208] 1,233,796[208] 1,659,440[208]
Campinas
Brazil 1,164,098[209] 3,094,181[209]
Ulsan
Korea, South 1,163,690[41]
Omsk
Russia 1,154,116[200]
Dakar
Senegal 1,146,053[210] 2,452,656[210]
Abu Dhabi
United Arab Emirates 1,145,000
Monterrey
Mexico 1,130,960 4,520,329
Tripoli
Libya 1,126,000 2,267,000 2,325,000
Rostov-on-Don
Russia 1,119,900[211]
T'bilisi
Georgia 1,118,035[212] 1,485,293
Fez
Morocco 1,112,072[213]
Birmingham
United Kingdom 1,111,300 3,683,000 2,440,986
Yerevan
Armenia 1,060,138[214]
Cologne
Germany 1,057,327[215] 3,573,500
Tunis
Tunisia 1,056,247 2,643,695 2,294,547
Astana
Kazakhstan 1,029,556[216] 1,200,000[217]
Islamabad
Pakistan 1,014,825[42] 1,829,180
See also[edit]
Geography portal
Lists portal
List of cities proper by population
List of towns and cities with 100,000 or more inhabitants
List of urban areas by population
List of metropolitan areas by population
List of largest cities throughout history
Notes[edit]
^ Sum of the 2014 population estimates for the "urban-function core district" and "urban-function extended district" of Chongqing, which were 3,677,600 and 4,512,200 respectively.[9] See also the next note.
^ Shanghai, Hangzhou, Nanjing, Suzhou, Wuxi, Ningbo, Changzhou, Shaoxing, and urban area of Zhangjiaggang-Jiangyin within the prefecture-level cities of Suzhou and Wuxi are treated as separate urban areas which constitute the Yangtze River Delta economic zone. Huai'an (1,856,000; 148 km2), Xuzhou (1,246,000; 233 km2), Nantong (1,036,000; 233 km2), Lianyungang (985,000; 155 km2), Zhenjiang (983,000; 168 km2), Yancheng (797,000; 207 km2), Huzhou (690,000; 111 km2), Taizhou (in Jiangsu Province; 300,000; 117 km2) and Suqian (220,000; 36 km2), as well as urban areas of Yangzhou (1,593,000; 233 km2) and Gaoyou (180,000; 39 km2) within the prefecture-level city of Yangzhou, urban areas of Kunshan (1,596,000; 492 km2), Changshu (1,139,000; 285 km2) and Taicang (523,000; 117 km2) within the prefecture-level city of Suzhou, urban areas of Cixi (1,200,000; 298 km2) and Yuyao (650,000; 122 km2) within the sub-provincial city of Ningbo, urban areas of Jiaxing (1,044,000; 259 km2) and Tongxiang (510,000; 52 km2) within the prefecture-level city of Jiaxing, urban areas of Wenling (510,000; 52 km2), Jiaojiang (375,000; 41 km2) and Huangyan (200,000; 34 km2) within the prefecture-level city of Taizhou (in Zhejiang Province), urban areas of Zhuji (500,000; 117 km2) and Shangyu (400,000; 158 km2) within the prefecture-level city of Shaoxing, urban areas of Yiwu-Dongyang (925,000; 233 km2), Jinhua (520,000; 186 km2), Yongkang (500,000; 223 km2), Dongyang (260,000; 104 km2) and Lanxi (220,000; 34 km2) within the prefecture-level city of Jinhua, and urban area of Fuyang (450,000; 49 km2) within the sub-provincial city of Hangzhou are also excluded.
^ Lagos consists 16 out of Lagos State's 20 LGA, which excludes: Badagry, Epe, Ibeju-Lekki and Ikorodu.[19][20]
^ Preliminary and disputed by all the major political parties in Sindh.[24][25][26]
^ Shenzhen, Dongguan and Foshan are all part of the Pearl River Delta, centered on Guangzhou.
^ Shenzhen, Dongguan and Foshan are all part of the Pearl River Delta, centered on Guangzhou.
^ Shenzhen, Dongguan and Foshan are all part of the Pearl River Delta, centered on Guangzhou.
^ The cities of Yokohama, Kawasaki and Saitama are all part of the Greater Tokyo Area
^ Quezon City and Caloocan City are both under the administration of Metropolitan Manila
^ Rome and its neighbouring comunes are all under the administration of Metropolitan City of Rome Capital
^ Davao City and its neighbouring cities and towns are all under part of Metropolitan Davao
^ Quezon City and Caloocan City are both under the administration of Metropolitan Manila
^ Kyoto and Kobe are both part of the Keihanshin, centered on Osaka.
^ The cities of Yokohama, Kawasaki and Saitama are all part of the Greater Tokyo Area
^ Kyoto and Kobe are both part of the Keihanshin, centered on Osaka.
^ Milan and its neighbouring comunes are all under the administration of Metropolitan City of Milan
^ The cities of Yokohama, Kawasaki and Saitama are all part of the Greater Tokyo Area
References[edit]
^ a b c d e "SOWC-2012-DEFINITIONS". UNICEF. Archived from the original on 8 December 2013. Retrieved 29 January 2014.
^ "World Urbanization Prospects: The 2007 Revision Population Database". Esa.un.org. Archived from the original on 22 August 2010. Retrieved 26 July 2010.
^ "United Nations Statistics Division – Demographic and Social Statistics". Millenniumindicators.un.org. Archived from the original on 23 June 2011. Retrieved 26 July 2010.
^ Demographic Yearbook 2005, Volume 57. United Nations. 2008. p. 241. ISBN 92-1-051099-2. Archived from the original on 2 May 2016.
^ a b World Urbanization Prospects: The 2003 Revision. United Nations. 2Remove "career" merge tag. I could not find a discussion on a merge.004. ISBN 92-1-151396-0. Archived from the original on 14 May 2016. Check date values in: |date= (help)
^ Alexander, Ruth (29 January 2012). "The world's biggest cities: How do you measure them?". BBC News. Archived from the original on 2 March 2015. Retrieved 16 March 2015.
^ a b Demographia (January 2015). Demographia World Urban Areas (PDF) (11 ed.). Archived (PDF) from the original on 26 December 2016. Retrieved 2 March 2015.
^ 2015年重庆常住人口3016.55万人 继续保持增长态势 [2016年重庆常住人口3670万人 继续保持增长态势] (in Chinese). Chongqing News. 28 January 2016. Archived from the original on 29 January 2016. Retrieved 13 February 2016.
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^ "Resident population by age, nationality and borough". City of Milan – Statistical Department. Archived from the original on 2 February 2017.
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External links[edit]
UNSD Demographics Statistics – City population by sex, city and city type
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† Aggregate urban areas are entire continuous built-up areas, grouping together contiguous cities (known as conurbations), whereas urban agglomerations are the built-up areas of individual cities.
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Displacement (vector)
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Classical mechanics
F → = m a → {\displaystyle {\vec {F}}=m{\vec {a}}}
Second law of motion
History
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Applied
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Formulations[show]
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Hamilton–Jacobi equation
Appell's equation of motion
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Core topics[show]
Damping (ratio)
Displacement
Equations of motion
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Scientists[show]
Galileo
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Clairaut
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Daniel Bernoulli
Johann Bernoulli
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v
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Displacement versus distance traveled along a path
A displacement is a vector whose length is the shortest distance from the initial to the final position of a point P.[1] It quantifies both the distance and direction of an imaginary motion along a straight line from the initial position to the final position of the point.
A displacement may be also described as a 'relative position': the final position of a point (Sf) relative to its initial position (Si), and a displacement vector can be mathematically defined as the difference between the final and initial position vectors:
s = S f − S i = Δ S {\displaystyle {\boldsymbol {s}}={\boldsymbol {S_{f}-S_{i}}}=\Delta {\boldsymbol {S}}}
In considering motions of objects over time the instantaneous velocity of the object is the rate of change of the displacement as a function of time. The instantaneous speed then is distinct from velocity, or the time rate of change of the distance traveled along a specific path. The velocity may be equivalently defined as the time rate of change of the position vector. If one considers a moving initial position, or equivalently a moving origin (e.g. an initial position or origin which is fixed to a train wagon, which in turn moves with respect to its rail track), the velocity of P (e.g. a point representing the position of a passenger walking on the train) may be referred to as a relative velocity, as opposed to an absolute velocity, which is computed with respect to a point which is considered to be 'fixed in space' (such as, for instance, a point fixed on the floor of the train station).
For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity. (Note that the average velocity, as a vector, differs from the average speed that is the ratio of the path length — a scalar — and the time interval.)
Contents
[hide]
1 Rigid body
2 Derivatives
3 See also
4 References
Rigid body[edit]
In dealing with the motion of a rigid body, the term displacement may also include the rotations of the body. In this case, the displacement of a particle of the body is called linear displacement (displacement along a line), while the rotation of the body is called angular displacement.
Derivatives[edit]
For a position vector s that is a function of time t, the derivatives can be computed with respect to t. These derivatives have common utility in the study of kinematics, control theory, vibration sensing and other sciences and engineering disciplines.
Velocity
v = d s d t {\displaystyle {\boldsymbol {v}}={\frac {{\text{d}}{\boldsymbol {s}}}{{\text{d}}t}}} (where ds is an infinitesimally small displacement)
Acceleration
a = d v d t = d 2 s d t 2 {\displaystyle {\boldsymbol {a}}={\frac {{\text{d}}{\boldsymbol {v}}}{{\text{d}}t}}={\frac {{\text{d}}^{2}{\boldsymbol {s}}}{{\text{d}}t^{2}}}}
Jerk
j = d a d t = d 2 v d t 2 = d 3 s d t 3 {\displaystyle {\boldsymbol {j}}={\frac {{\text{d}}{\boldsymbol {a}}}{{\text{d}}t}}={\frac {{\text{d}}^{2}{\boldsymbol {v}}}{{\text{d}}t^{2}}}={\frac {{\text{d}}^{3}{\boldsymbol {s}}}{{\text{d}}t^{3}}}}
These common names correspond to terminology used in basic kinematics.[2] By extension, the higher order derivatives can be computed in a similar fashion. Study of these higher order derivatives can improve approximations of the original displacement function. Such higher-order terms are required in order to accurately represent the displacement function as a sum of an infinite series, enabling several analytical techniques in engineering and physics. The fourth order derivative is called jounce.
See also[edit]
Equipollence (geometry)
Position vector
Affine space
References[edit]
Jump up ^ Tom Henderson. "Describing Motion with Words". The Physics Classroom. Retrieved 2 January 2012.
Jump up ^ Stewart, James (2001). "§2.8 - The Derivative As A Function". Calculus (2nd ed.). Brooks/Cole. ISBN 0-534-37718-1.
[show]
v
t
e
Kinematics
← Integrate … Differentiate →
Absement
Displacement (Distance)
Velocity (Speed)
Acceleration
Jerk
Jounce
[show]
v
t
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Classical mechanics SI units
Linear/translational quantities Angular/rotational quantities
Dimensions
1
L
L2
Dimensions
1
1
1
T
time: t
s absement: A
m s
T
time: t
s
1
distance: d, position: r, s, x, displacement
m area: A
m2
1
angle: θ, angular displacement: θ
rad solid angle: Ω
rad2, sr
T−1
frequency: f
s−1, Hz speed: v, velocity: v
m s−1 kinematic viscosity: ν,
specific angular momentum: h
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frequency: f
s−1, Hz angular speed: ω, angular velocity: ω
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kg m s−1, N s action: 𝒮, actergy: ℵ
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ML2T−1
angular momentum: L, angular impulse: ΔL
kg m2 s−1 action: 𝒮, actergy: ℵ
kg m2 s−1, J s
MT−2
force: F, weight: Fg
kg m s−2, N energy: E, work: W
kg m2 s−2, J
ML2T−2
torque: τ, moment: M
kg m2 s−2, N m energy: E, work: W
kg m2 s−2, J
MT−3
yank: Y
kg m s−3, N s−1 power: P
kg m2 s−3, W
ML2T−3
rotatum: P
kg m2 s−3, N m s−1 power: P
kg m2 s−3, W
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Chess clock
From Wikipedia, the free encyclopedia
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For the instrument or person who keeps track of the time during a sporting event, see Timekeeper.
A chess clock consists of two adjacent clocks with buttons to stop one clock while starting the other, so that the two clocks never run simultaneously. Chess clocks are used in chess and other two-player games where the players move in turn. The purpose is to keep track of the total time each player takes for his or her own moves, and ensure that neither player overly delays the game.
Chess clocks were first used extensively in tournament chess, and are often called game clocks. The first time that game clocks were used in a chess tournament was in the London 1883 tournament.[1] Their use has since spread to tournament Scrabble, shogi, go, and nearly every competitive two-player board game, as well as other types of games. In a tournament, the arbiter typically places all clocks in the same orientation, so that they can easily assess games that need attention at later stages.
The simplest time control is "sudden death", in which players must make a predetermined number of moves in a certain amount of time or forfeit the game immediately. A particularly popular variant in informal play is blitz chess, in which each player is given a short time (e.g. five minutes) on the clock in which to play the entire game.
The players may take more or less time over any individual move. The opening moves in chess are often played quickly due to their familiarity, which leaves the players more time to consider more complex and unfamiliar positions later. It is not unusual in slow chess games for a player to leave the table, but the clock of the absent player continues to run if it is their turn, or starts to run if their opponent makes a move.
Contents
[hide]
1 Analog game clocks
2 Early development of digital game clocks
3 Fischer clock and related designs
4 Timing methods
5 See also
6 References
7 Further reading
8 External links
Analog game clocks[edit]
A typical analog chess clock
Analog clocks are equipped with a "flag" that falls to indicate the exact moment the player's time has expired. Analog clocks use mechanical buttons. Pressing the button on one player's side physically stops the movement of that player's clock and releases the hold on the opponent's.
The drawbacks of the mechanical clocks include accuracy and matching of the two clocks, and matching of the indicators (flags) of time expiration. Additional time cannot easily be added for more complex time controls, especially those that call for an increment or delay on every move, such as some forms of byoyomi. However, a malfunctioning analog clock is a less serious event than a malfunctioning digital clock.[2]
Early development of digital game clocks[edit]
Modern day chess clocks.
In 1973, to address the issues with analog clocks, Bruce Cheney, a Cornell University Electrical Engineering student and chess player, created the first digital chess clock as a project for an undergraduate EE course.[3] Typical of most inventions, it was crude compared to the products on the market many years later and was limited by the technology that existed at the time. For example, the display was done with red LEDs. LEDs require significant power, and as a result, the clock had to be plugged into a wall outlet. The high cost of LEDs at the time meant that only one set of digits could be displayed, that of the player whose turn it was to move. This meant that each player's time had to be multiplexed to the display when their time was running. In 1973, LSI chips were not readily or cheaply available, so all the multiplexing and logic were done using chips that consisted of four two-input TTL NAND gates, which resulted in excessive power consumption. Being plugged into the wall is obviously a major drawback, but had one advantage: the timebase for the clock was driven off of a rectified version of 60 cycle AC current. Each player had a separate counter, and, in a parallel to the original mechanical architecture, one player's counter was disabled while the other's was running. The clock only had one mode: time ran forward. It could be reset, but not set. It did not count the number of moves. But it successfully addressed the original goals of the project (accurate and matched timing).
The first commercially available digital chess clock was patented in 1975 by Joseph Meshi and Jeffrey R. Ponsor and sold as the Micromate-80.[4] Three years later a much-improved Micromate-180 was produced alongside Meshi's MBA Thesis, "Demand Analysis for a New Product (The Digital Chess Clock)", at San Diego State University, while Meshi and Ponsor continued to develop digital gaming.[5]
Fischer clock and related designs[edit]
Digital chess clock connected to a board that automatically senses when moves have been made
Digital clocks and Internet gaming have spurred a wave of experimentation with more varied and complex time controls than the traditional standards. Time control is commonly used in modern chess in many different methodologies. One particularly notable development, which has gained quite wide acceptance in chess, was proposed by former world champion Bobby Fischer, who in 1988 filed for U.S. Patent 4,884,255 (awarded in 1989) for a new type of digital chess clock. Fischer's digital clock gave each player a fixed period of time at the start of the game and then added a small amount after each move. Joseph Meshi called this "Accumulation" as it was a main feature of his patented Micromate-180 (US Patent 4,247,925 1978). This became the linchpin of Fischer's clock patented 10 years later. In this way, the players would never be desperately short of time.
The increment time control was first used in the privately organised 1992 Fischer–Spassky match, and quickly became popular in the wider chess world, and was used in the FIDE World Chess Championship 1998.[6] As of 2017 most top level tournaments use Fischer's system as well as an increasing number of lower level tournaments. Other aspects of Fischer's patent, such as a synthesized voice announcing how much time the players have, thus eliminating the need for them to keep looking at the clock, have not been adopted.
On March 10, 1994, a patent application was filed by inventors Frank A. Camaratta Jr. of Huntsville, Alabama, and William Goichberg of Salisbury Mills, New York, for a game timer especially suitable for playing the game of chess, which employed a "delay" feature. The game timer provides, among other features, a user-definable delay between the time the activation button is pressed and the time that the activated clock actually begins to count down. United States Patent 5,420,830 was issued on May 10, 1995, and subsequently assigned to the United States Chess Federation by the inventors. As with the Fischer clock, the benefit of the delay clock is to reduce the likelihood that a player with positional and/or material superiority will lose a match solely because of the expiration of time on that player's time clock. Delay is still popular in the U.S, although increment is becoming more popular in the US.
Timing methods[edit]
Main article: Time control
There are three main types of chess timing methods, two of which are mathematically equivalent: (1) Increment (invented by Bobby Fischer), (2) Bronstein delay (invented by David Bronstein), and (3) Simple delay.
Increment (also known as Fischer and bonus)—a specified amount of time is added for each move. For example, if the increment is thirty seconds, each player gets an additional thirty seconds for each move. Under FIDE and US Chess rules you get the increment for move one as well. For example, for G/3;inc2 (three minutes of base time with a two second increment each move), you start with three minutes and two seconds on the first move. Not all digital chess clocks automatically give the increment for move one and thus for those that don't, the increment time has to be added manually to be base time so each player gets the increment for move one.
Bronstein delay—this timing method adds time but unlike increment not always the maximum amount of time is added. If a player expends more than the specified delay, then the entire delay is added to the player's clock but if a player moves faster than the delay, only the exact amount of time expended by the player is added. For example, if the delay is ten seconds and a player uses ten or more seconds for a move, ten seconds is added after they complete their move. If the player uses five seconds for a move, five seconds is added after they complete their move. This ensures that the base time left on the clock can never increase even if a player makes fast moves. As with increment, you get the delay time for move one under FIDE and US Chess rules.
Simple delay (also known as countdown delay and US delay)—with this timing method, the clock waits for the delay period each move before starting to subtract the player's base time. For example, if the delay is ten seconds, the clock waits for ten seconds each move before the base time starts going down. This timing method is mathematically equivalent to Bronstein delay. Simple delay is the form of delay most often used in the US while Bronstein delay is the form of delay most often used in most other countries.
See also[edit]
Chess equipment
References[edit]
Jump up ^ Vidmar, Milan (1960). Goldene Schachzeiten: Erinnerungen. W. de Gruyter. p. 10. ISBN 3-11-002095-5.
Jump up ^ "FAQ (Starting Out) - Learn About Chess". United States Chess Federation. 1999-11-30. Retrieved 2008-01-19.
Jump up ^ "Early Bird", Chess Life, April 1992.
Jump up ^ US patent 4062180, Meshi, Joseph & Ponsor, Jeffrey R., "Electronic chess clock", issued 1977-12-13 ; filed July 1975.
Jump up ^ US patent 4247925, Meshi, Joseph & Ponsor, Jeffrey R., "Game microcomputer", issued 1981-01-27 ; filed January 1978.
Jump up ^ The Week in Chess 161, The Week in Chess, 8-Dec-1997
Further reading[edit]
Keith Ammann (April 2012). "Winding Down: This year's rule changes may begin the last chapter in the history of the analog clock". Chess Life.
External links[edit]
Wikimedia Commons has media related to Chess clocks.
Look up chess clock in Wiktionary, the free dictionary.
U.S. Patent 4,884,255 for Fischer's clock
Online Chess Clock / Chess Timer Example, used for Fast Chess
Online chess clock that implements Fischer and Bronstein timing methods
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values: ساعة الشطرنج – Arabic

values: Шахматны гадзіннік – Belarusian

values:
https://da.wikipedia.org/wiki/Skakur
Skakur – Danish
da
da
interlanguage-link-target

values:
https://de.wikipedia.org/wiki/Schachuhr
Schachuhr – German
de
de
interlanguage-link-target

values: interlanguage-link interwiki-de badge-Q17437798 badge-goodarticle

values:
https://et.wikipedia.org/wiki/Malekell
Malekell – Estonian
et
et
interlanguage-link-target

values: שעון שחמט – Hebrew

values: Шаховски часовник – Macedonian

values:
https://no.wikipedia.org/wiki/Sjakkur
Sjakkur – Norwegian
no
no
interlanguage-link-target

values: Шахматные часы – Russian

values: Шаховски сат – Serbian

values: ஆட்டக் கடிகாரம் – Tamil

values: Шаховий годинник – Ukrainian

values: شطرنج گھڑی – Urdu

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