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Central place theory

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most efficient transport network. There are maximum central places possible located on the main transport routes connecting the higher order center. The transportation principle involves the minimization of the length of roads connecting central places at all hierarchy levels. In this system of nesting, the lower order centres are all located along the roads linking the higher order centres. This alignment of places along a road leads to minimization of road length. However, for each higher order centre, there are now four centres of immediate lower order, as opposed to three centres under the marketing principle.
672: 210: 362:, who asserted that settlements simply functioned as 'central places' providing economic services to surrounding areas. Christaller explained that a large number of small settlements will be situated relatively close to one another for efficiency, and because people don't want to travel far for everyday needs, like getting bread from a bakery. But people would travel further for more expensive and infrequent purchases or specialized goods and services which would be located in larger settlements that are farther apart. 135: 825:(see K=4 above) usually have six thoroughfares through them—the thoroughfares including highways, rivers, railroads, and canals. They are most efficient and can deliver the lowest cost services because transportation is cheaper. Those having settled on the market principle (K=3 above) have more expensive services and goods, as they were founded at times when transportation was more primitive. In Appalachia, for example, the market principle still prevails and rural medical care is much more expensive. 228: 510: 2207: 601:= 7 administrative principle (or political-social principle), settlements are nested according to sevens. The market areas of the smaller settlements are completely enclosed within the market area of the larger settlement. Since tributary areas cannot be split administratively, they must be allocated exclusively to a single higher-order place. Efficient administration is the control principle in this hierarchy. 561: 36: 2195: 295: 587: 2229: 77: 873:
Smith was able to delineate medical care regions (the range), describe the hierarchy of medical services, the population base required of each medical specialty (threshold), the efficiency of regions, and the importance of how an area was settled to the delivery of medical care, that is, according to
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Closure problem. Christaller's original scheme implies an infinite landscape. Although each market has finite size, the total system has no boundaries to it. Neither Christaller, nor the early related literature provide any guidance as to how the system can be "contained". Openshaw and Veneris (2003)
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For example, orthopedic surgeons are found in ski areas, obstetricians in the suburbs, and boutique specialties such as hypnosis, plastic surgery, psychiatry are more likely to be found in high income areas. It was possible to estimate the size of population (threshold) needed to support a specialty,
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Christaller also erred in the assumption that cities "emerge". In California and much of the United States, many cities were situated by the railroads at the time the tracks were laid. In California, towns founded by the railroads were 12 miles apart, the amount of track a section crew could maintain
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At the base of the hierarchy pyramid are shopping centres, newsagents etc. which sell low order goods. These centres are small. At the top of the pyramid are centres selling high order goods. These centres are large. Examples for low order goods and services are: newspaper stalls, groceries, bakeries
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Openshaw and Veneris (2003) succeeded in linking these two major regional theories in a clear and theoretically consistent way: using the data they derived from the operationalization of CPT, they experimented with several SIM. Following a thorough investigation via computer simulation, they reached
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Calculating inter- and intra-zonal costs/distances. Christaller assumed freedom of movement in all directions, which would imply "airline" distances between centres. At the same time, he provided specific road networks for the CP system, which do not allow for airline distances. This is a major flaw
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Newer theoretical developments have shown that it is possible to overcome the static aspect of CPT. Veneris (1984) developed a theoretical model which starts with (a) a system of evenly distributed ("medieval") towns; (b) new economic activities are located in some towns thus causing differentiation
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CPT is often criticized as being "unrealistic". However, several studies show that it can describe existing urban systems. An important issue is that Christaller's original formulation is incorrect in several ways (Smith). These errors become apparent if we try to make CPT "operational", that is if
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Economic status of consumers in an area is also important. Consumers of higher economic status tend to be more mobile and therefore bypass centers providing only lower order goods. The application of central place theory must be tempered by an awareness of such factors when planning shopping center
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The validity of the place theory may vary with local factors, such as climate, topography, history of development, technological improvement and personal preference of consumers and suppliers. However, it is still possible to discern Christaller patterns in most distributions of urban centres, even
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In the orderly arrangement of an urban hierarchy, seven different principal orders of settlement have been identified by Christaller, providing different groups of goods and services. Settlement are regularly spaced - equidistant spacing between same order centers, with larger centers farther apart
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K' 4 transport principle, the market area of a higher-order place includes a half of the market area of each of the six neighbouring lower-order places, as they are located on the edges of hexagons around the high-order settlements. This generates a hierarchy of central places which results in the
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In medical care regions described by Smith, there is a hierarchy of services, with primary care ideally distributed throughout an area, middle sized cities offering secondary care, and metropolitan areas with tertiary care. Income, size of population, population demographics, distance to the next
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The central place theory has been criticized for being static; it does not incorporate the temporal aspect in the development of central places. Furthermore, the theory holds up well when it comes to agricultural areas, but not industrial or postindustrial areas due to their diversified nature of
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Her work is important for the study of physician location—where physicians choose to practice and where their practices will have a sufficient population size to support them. The income level of the population determines whether sufficient physicians will practice in an area and whether public
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The result of these consumer preferences is that a system of centers of various sizes will emerge. Each center will supply particular types of goods forming levels of hierarchy. In the functional hierarchies, generalizations can be made regarding the spacing, size and function of settlements.
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offered there was more important as a measure of the importance of a city in attracting consumers. In applying CPT to describe the delivery of medical care in California, Smith counted the number of physician specialties to determine the importance of a city in the delivery of medical care.
663:(higher order); district and local shopping centers supply, increasingly, convenience (lower order) goods. These centers provided for in the new town plan are not free from outside competition. The impacts of surrounding existing centers on the new town centers cannot be ignored. 754:
Another example of the use of CPT was in the delineation of Medical Care Regions in California. A hierarchy of primary, secondary and tertiary care cities was described, and the population size and income needed to support each medical care specialty in California determined.
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According to Margot Smith, Walter Christaller erred in his development of CPT in 1930 by using size of population and number of telephones in determining the importance of a city. Smith recognized that although population size was important to the area served by a city, the
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we try to derive numerical data out of the theoretical schemata. These problems have been identified for by Veneris (1984) and subsequently by Openshaw and Veneris (2003), who provided also theoretically sound and consistent solutions, based on a K=3, 37-centre CP system:
524:= 3, the market area of a higher-order place (node) occupies one-third of the market area of each of the consecutive lower size place (node) that lies on its neighbour; the lower size nodes (6 in numbers and second larger circles) are located at the corner of a largest 865:
It was once thought that central place theory is not compatible with spatial interaction models (SIM). It is paradoxical however that some times towns or shopping centres are planned with CPT, and subsequently evaluated with SIM.
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is a good example of a K=4 Transport Model Central Place, although it is surrounded by 7, rather than 6, settlements. Each satellite is 10–15 miles from Cambridge and each lies on a major road leading out of Cambridge:
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Purchasing power and density affect the spacing of centers and hierarchical arrangements. Sufficient densities will allow, for example, a grocery store, a lower order function, to survive in an isolated location.
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in the 1850s; larger towns were 60 miles apart, the distance a steam engine could travel before needing water. Older towns were founded a day's horse ride apart by the Spanish priests who founded early missions.
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of the Netherlands provide an isotropic plane on which settlements have developed and in certain areas 6 small towns can be seen surrounding a larger town, especially in the Noord-Oostpolder and Flevoland.
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The higher the order of the goods and services (more durable, valuable and variable), the larger the range of the goods and services, the longer the distance people are willing to travel to acquire them.
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Smith, Margot W. The Distribution of Medical Care in Central California: a Social and Economic Analysis, Thesis, School of Public Health, University of California, Berkeley, 1977 - 1004 pages
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Market area studies provide another technique for using central place theory as a retail location planning tool. The hierarchy of shopping centers has been widely used within the planning of "
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Smith, Margot W. Physician's Specialties and Medical Trade Areas: An Application of Central Place Theory. Papers and Proceedings of Applied Geography Conferences, Vol. 9, West Point NY 1986.
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which neither Christaller, nor early related literature have identified. Openshaw and Veneris (2003) calculate costs/distances which are consistent with the Christallerian principles.
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though these patterns will often be distorted by the terrain or imperfect because of suboptimal (with regard to the optimal distribution of centres) historical development decisions.
498:-values which show how much the sphere of influence of the central places takes in — the central place itself counts as 1 and each portion of a satellite counts as its portion: 323: 479:
and post offices. Examples for high order goods and services include jewelry, large shopping malls and arcades. They are supported by a much larger threshold population and demand.
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identified three different types of closure, namely (a) isolated state, (b) territorial closure and (c) functional closure. Each closure type implies different population patterns.
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and also to link specialties that needed to cooperate and locate near each other, such as hematology, oncology, and pathology, or cardiology, thoracic surgery and pulmonology.
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As all of the satellite settlements are on transport links, this is a good example of a K=4 CPT model (although in this case it is K=4.5 due to 7 rather than 6 settlements).
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The larger the settlements grow in size, the greater the distance between them, i.e. villages are usually found close together, while cities are spaced much further apart.
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Generating trips. Following the basic Christallerian logic and the closure types identified, Openshaw and Veneris (2003) calculate trip patterns between the 27 centres.
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The distribution of medical care in California followed patterns having to do with the settlement of cities. Cities and their hinterlands having characteristics of the
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Smith, Margot W. A Guide to the Delineation of Medical Care Regions, Medical Trade Areas and Hospital Service Areas. Public Health Reports, 94:3:247 May 1979
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Range is the maximum distance consumers are prepared to travel to acquire goods - at some point the cost or inconvenience will outweigh the need for the good.
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Openshaw S, Veneris Y, 2003, "Numerical experiments with central place theory and spatial interaction modelling" Environment and Planning A 35(8) 1389–1403 (
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He deduced that settlements would tend to form in a triangular/hexagonal lattice, as it is the most efficient pattern to serve areas without any overlap.
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As a settlement increases in size, the number of higher-order services will also increase, i.e. a greater degree of specialization occurs in the services.
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and evolution into a hierarchical ("industrial") city system; (c) further differentiation leads into a post-hierarchical ("postindustrial") city system.
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Smith, Margot W. The Economics of Physician Location, Western Regional Conference, American Association of Geographers, Chicago, Illinois, 1979
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around low value the high-order settlement. Each high-order settlement gets one-third of each satellite settlement (which are 6 in total), thus
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The larger the settlements are in size, the fewer in number they will be, i.e. there are many small villages, but few large cities.
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Consumers visit the nearest central places that provide the function which they demand. They minimize the distance to be travelled
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Veneris, Y, 1984, Informational Revolution, Cybernetics and Urban Modelling, PhD Thesis, University of Newcastle upon Tyne, UK.
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service center, all had an influence on the number and kind of specialists located in a population center. (Smith, 1977, 1979)
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Therefore, the trade areas of these central places who provide a particular good or service must all be of equal size
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than smaller centers. Settlements have hexagonal market areas, and are most efficient in number and functions.
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is the minimum market (population or income) needed to bring about the selling of a particular good or service.
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no provider of goods or services is able to earn excess profit (each supplier has a monopoly over a hinterland)
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in the UK also provide a large expanse of flat land with no natural barriers to settlement development.
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This evolution can be modelled by means of the three major CPT theories: stage (a) is a system of
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that seeks to explain the number, size and range of market services in a commercial system or
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These assumptions generally mean that the theory has no utility beyond abstract discussions.
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As a settlement increases in size, the range and number of its functions will increase .
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shows settlements in different levels that are consistent with the Central place theory
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there is only one type of transport and this would be equally easy in all directions
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perfect competition and all sellers are economic people maximizing their profits
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The references used may be made clearer with a different or consistent style of
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To develop the theory, Christaller made the following simplifying assumptions:
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Goodall, B. (1987) The Penguin Dictionary of Human Geography. London: Penguin.
644: 247: 647:: high mobility afforded by the automobile allows overlapping of market areas 2143: 1773: 1616: 700: 655:". In this new town, the hierarchy of business centers is evident. One main 378: 340: 628:: industrial areas can provide little in the way of a consuming population 1595: 1585: 1557: 1525: 1478: 1217: 1135: 1130: 738: 692: 652: 625: 407: 391:
all settlements are equidistant and exist in a triangular lattice pattern
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various services or their varied distribution of natural resources.
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have a similar purchasing power and demand for goods and services.
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consumers are of the same income level and same shopping behaviour
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post-hierarchical system. Furthermore, stage (b) corresponds to
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The importance of a city and other theoretical considerations
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transport cost is directly proportional to distance travelled
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subsidy is needed to maintain the health of the population.
641:: this limits the extent of market areas in all directions 549:= 3 marketing network the distance traveled is minimized. 1018:
Walter Christaller: Hierarchical Patterns of Urbanization
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Geographical theory of spatial distribution of cities
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The different layouts predicted by Christaller have
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Central place theory and spatial interaction models
870:important theoretical and practical conclusions. 874:traffic, market or administrative principles. 1053: 1013:Walter Christaller's Theory of Central Places 768:Newer developments: a dynamic concept for CPT 621:Factors shaping the extent of market areas: 317: 8: 935: 933: 931: 381:(all flat), homogeneous, limitless surface ( 717:- A1303 (now bypassed by A14/A11) northeast 64:Learn how and when to remove these messages 1999: 1795: 1380: 1170: 1060: 1046: 1038: 324: 310: 215: 532: = 1 + 6 Ă—  197:Learn how and when to remove this message 179:Learn how and when to remove this message 117:Learn how and when to remove this message 1268:Regional Planning Association of America 434:The theory then relied on two concepts: 142:This article includes a list of general 927: 829:Making central place theory operational 270: 234: 218: 910:Boundary problem (in spatial analysis) 520:According to the marketing principle 7: 2228: 1339:Professional transportation planner 1023:Christaller's Central Place Theory 556:= 4 transporting/traffic principle 148:it lacks sufficient corresponding 25: 45:This article has multiple issues. 2227: 2206: 2205: 2193: 388:an evenly distributed population 293: 226: 133: 75: 34: 1736:Transferable development rights 1291:Environmental impact assessment 53:or discuss these issues on the 1362:Community economic development 1141:Planning and zoning commission 1: 1975:Planning Accreditation Board 1334:Transit-oriented development 1296:Recreation resource planning 582:= 7 administrative principle 394:evenly distributed resources 284:Cities by population density 915:Unified settlement planning 799:number of kinds of services 2292: 1987:Professional organizations 1344:Urban freight distribution 1319:Transportation forecasting 1028:Christaller - Course notes 854: 2223:List of planning journals 2187: 1192:History of urban planning 1075: 2159:Marine spatial planning 1671:Healthy community design 1249:Village design statement 1239:Preservation development 1234:Conservation development 953:. 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386: 383:abstract space 367: 364: 332: 331: 329: 328: 321: 314: 306: 303: 302: 289: 288: 287: 286: 281: 279:Largest cities 273: 272: 268: 267: 266: 265: 260: 255: 250: 245: 237: 236: 232: 231: 223: 222: 205: 204: 187: 186: 141: 139: 132: 125: 124: 88:citation style 83: 81: 74: 69: 43: 42: 40: 33: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 2288: 2277: 2274: 2272: 2269: 2267: 2264: 2262: 2259: 2257: 2254: 2253: 2251: 2236: 2235: 2226: 2224: 2221: 2219: 2216: 2214: 2213: 2204: 2202: 2201: 2190: 2189: 2186: 2180: 2177: 2175: 2172: 2170: 2169:Public policy 2167: 2165: 2164:Public health 2162: 2160: 2157: 2155: 2152: 2150: 2147: 2145: 2142: 2140: 2137: 2135: 2134:Urban ecology 2132: 2130: 2127: 2125: 2122: 2120: 2117: 2116: 2114: 2108: 2098: 2097:Ancient Egypt 2095: 2093: 2090: 2088: 2085: 2083: 2080: 2079: 2077: 2073: 2067: 2064: 2062: 2059: 2057: 2054: 2053: 2051: 2047: 2041: 2038: 2036: 2033: 2031: 2028: 2026: 2023: 2021: 2018: 2016: 2013: 2011: 2008: 2007: 2005: 2001: 1998: 1994: 1988: 1985: 1981: 1978: 1976: 1973: 1972: 1971: 1968: 1967: 1965: 1961: 1951: 1948: 1946: 1945:Lewis Mumford 1943: 1941: 1938: 1936: 1933: 1931: 1928: 1927: 1925: 1921: 1915: 1914: 1911: 1908: 1906: 1903: 1901: 1898: 1896: 1895:Raymond Unwin 1893: 1891: 1888: 1886: 1883: 1881: 1878: 1876: 1873: 1871: 1868: 1866: 1863: 1861: 1858: 1856: 1853: 1851: 1848: 1846: 1843: 1841: 1838: 1836: 1833: 1831: 1828: 1826: 1823: 1821: 1818: 1816: 1813: 1811: 1808: 1807: 1805: 1803: 1802:practitioners 1797: 1794: 1790: 1780: 1777: 1775: 1771: 1768: 1766: 1763: 1761: 1758: 1756: 1752: 1749: 1747: 1744: 1742: 1739: 1737: 1734: 1732: 1731:Tract housing 1729: 1727: 1724: 1722: 1721:Temporary use 1719: 1717: 1714: 1712: 1709: 1707: 1706:Planning gain 1704: 1702: 1699: 1697: 1694: 1692: 1689: 1687: 1684: 1682: 1679: 1677: 1674: 1672: 1668: 1665: 1663: 1660: 1658: 1654: 1651: 1649: 1646: 1643: 1640: 1638: 1637:Creative city 1635: 1633: 1630: 1628: 1625: 1623: 1620: 1618: 1615: 1613: 1610: 1609: 1607: 1603: 1597: 1594: 1592: 1591:Urban village 1589: 1587: 1584: 1582: 1579: 1576: 1573: 1571: 1570:Model village 1568: 1564: 1561: 1560: 1559: 1556: 1552: 1549: 1548: 1547: 1544: 1542: 1539: 1537: 1534: 1532: 1531:Commuter town 1529: 1527: 1523: 1520: 1519: 1517: 1515: 1511: 1505: 1504:Urban renewal 1502: 1500: 1497: 1495: 1492: 1490: 1487: 1485: 1482: 1480: 1477: 1475: 1472: 1470: 1467: 1466: 1464: 1462: 1458: 1452: 1449: 1447: 1444: 1442: 1441:Structuralism 1439: 1437: 1434: 1432: 1429: 1427: 1424: 1422: 1419: 1417: 1414: 1412: 1409: 1407: 1404: 1402: 1399: 1397: 1394: 1392: 1389: 1388: 1386: 1382: 1379: 1373: 1363: 1360: 1359: 1357: 1355: 1351: 1345: 1342: 1340: 1337: 1335: 1332: 1330: 1327: 1325: 1322: 1320: 1317: 1316: 1314: 1312: 1308: 1302: 1299: 1297: 1294: 1292: 1289: 1287: 1284: 1283: 1281: 1279: 1275: 1269: 1266: 1265: 1263: 1261: 1257: 1250: 1247: 1245: 1244:Rural housing 1242: 1240: 1237: 1235: 1232: 1231: 1229: 1225: 1219: 1216: 1214: 1211: 1209: 1206: 1204: 1203:Redevelopment 1201: 1198: 1195: 1193: 1190: 1187: 1184: 1182: 1179: 1178: 1176: 1172: 1169: 1163: 1157: 1154: 1152: 1149: 1147: 1144: 1142: 1139: 1137: 1134: 1132: 1129: 1127: 1124: 1122: 1119: 1117: 1114: 1112: 1109: 1108: 1106: 1102: 1096: 1093: 1091: 1088: 1086: 1083: 1081: 1078: 1077: 1074: 1070: 1063: 1058: 1056: 1051: 1049: 1044: 1043: 1040: 1034: 1031: 1029: 1026: 1024: 1021: 1019: 1016: 1014: 1011: 1010: 1006: 1001: 998: 995: 992: 989: 986: 983: 982: 978: 966: 960: 957: 952: 945: 942: 936: 934: 932: 928: 921: 916: 913: 911: 908: 906: 903: 901: 898: 896: 893: 891: 888: 886: 883: 882: 877: 875: 871: 867: 862: 861:Gravity model 858: 850: 844: 841: 837: 836: 835: 828: 826: 824: 819: 815: 811: 807: 803: 800: 791: 789: 787: 783: 779: 774: 767: 765: 758: 756: 752: 746: 743: 740: 737: 734: 731: 729:- A1301 south 728: 725: 722: 719: 716: 713: 710: 707: 706: 705: 702: 698: 694: 689: 686: 678: 673: 666: 664: 662: 661:durable goods 658: 654: 646: 643: 640: 637: 634: 633:accessibility 630: 627: 624: 623: 622: 619: 615: 611: 604: 602: 600: 597:According to 593:= 7 principle 592: 588: 581: 578: 576: 575: 571:According to 567:= 4 principle 566: 562: 555: 552: 550: 548: 543: 531: 527: 523: 516:= 3 principle 515: 511: 504: 501: 499: 497: 492: 488: 482: 480: 476: 469: 466: 463: 460: 459: 458: 451: 448: 445: 444: 443: 441: 437: 432: 426: 423: 422: 421: 415: 412: 409: 405: 402: 399: 396: 393: 390: 387: 384: 380: 377:an unbounded 376: 375: 374: 371: 365: 363: 361: 357: 353: 349: 345: 342: 338: 327: 322: 320: 315: 313: 308: 307: 305: 304: 301: 291: 290: 285: 282: 280: 277: 276: 275: 274: 269: 264: 261: 259: 256: 254: 251: 249: 246: 244: 241: 240: 239: 238: 233: 229: 225: 224: 221: 217: 211: 201: 198: 183: 180: 172: 162: 158: 152: 151: 145: 140: 131: 130: 121: 118: 110: 107:February 2016 100: 96: 90: 89: 84:This article 82: 73: 72: 67: 65: 58: 57: 52: 51: 46: 41: 32: 31: 19: 2233: 2210: 2191: 2119:Architecture 2092:Nazi Germany 1900:Thomas Adams 1880:Loretta Lees 1875:Le Corbusier 1845:Edmund Bacon 1810:AndrĂ©s Duany 1765:Urbanization 1751:Urban sprawl 1716:Rural flight 1696:Permeability 1691:Model cities 1563:Logging camp 1522:Company town 1436:Smart growth 1426:New Urbanism 1208:Urban design 959: 950: 944: 872: 868: 864: 832: 822: 820: 816: 812: 808: 804: 798: 795: 775: 771: 762: 753: 750: 690: 682: 650: 620: 616: 612: 608: 598: 596: 590: 579: 572: 570: 564: 553: 546: 544: 529: 521: 519: 513: 502: 495: 493: 489: 486: 477: 473: 455: 439: 435: 433: 430: 419: 372: 369: 341:geographical 339:is an urban 336: 335: 193: 175: 166: 147: 113: 104: 85: 61: 54: 48: 47:Please help 44: 2112:disciplines 1935:Jane Jacobs 1860:James Rouse 1741:Urban decay 1726:Third place 1701:Placemaking 1551:Pit village 1541:Global city 741:- A428 west 711:- A10 north 697:East Anglia 639:Competition 483:Predictions 358:geographer 258:Megalopolis 243:Conurbation 161:introducing 2250:Categories 1855:Ian McHarg 1800:Theorists/ 1577:(New town) 1536:Ghost town 1375:Concepts/ 1111:Urban area 979:References 905:Zipf's law 778:von ThĂĽnen 645:Technology 605:Evaluation 248:Metropolis 144:references 99:footnoting 50:improve it 2144:Geography 2056:Barcelona 2035:Singapore 2010:Australia 2003:Countries 1617:Cityscape 1384:Movements 759:Criticism 721:Haverhill 715:Newmarket 701:Cambridge 653:new towns 447:Threshold 436:threshold 408:consumers 379:isotropic 169:July 2023 56:talk page 2212:Category 2061:Shanghai 1963:Training 1605:Concepts 1596:Boomtown 1586:Arcology 1558:Man camp 1526:Monotown 1479:Ekistics 1461:Theories 1377:theories 1218:Urbanism 1167:branches 1136:Planning 1131:Land use 1085:Theories 878:See also 782:Löschian 739:St Neots 667:Examples 626:Land use 253:Megacity 220:Ekistics 95:citation 2234:Commons 2110:Related 1923:Critics 1676:LEED-ND 1174:General 1104:General 1095:Outline 1080:History 895:Fractal 745:St Ives 733:Royston 685:polders 537:⁄ 526:hexagon 157:improve 2082:Africa 2066:Sydney 2049:Cities 2030:Serbia 2025:Russia 1996:Places 1792:People 1779:Zoning 1662:Infill 1126:Suburb 356:German 344:theory 146:, but 2075:Other 2015:China 1451:YIMBY 1421:NIMBY 1227:Rural 1199:(Eur) 1165:Major 1090:Index 968:(PDF) 922:Notes 631:Poor 440:range 350:in a 271:Lists 1644:(US) 1251:(UK) 1188:(US) 1116:City 859:and 693:Fens 691:The 438:and 406:all 97:and 709:Ely 695:of 442:. 2252:: 1772:/ 1753:/ 1669:/ 1655:/ 1524:/ 930:^ 59:. 1061:e 1054:t 1047:v 987:) 970:. 599:K 591:K 580:K 565:K 554:K 547:K 539:3 535:1 530:K 522:K 514:K 503:K 496:K 385:) 325:e 318:t 311:v 200:) 194:( 182:) 176:( 171:) 167:( 153:. 120:) 114:( 109:) 105:( 101:. 91:. 66:) 62:( 20:)

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