Abstract
The ‘compact city’ concept is prominent in contemporary planning policy debates about ideal urban forms. However, the property of compactness itself is not well defined, and is sometimes confused or conflated with density. This chapter develops a new geometric interpretation of compactness with specific indicators—relating to diameter and perimeter—that can capture this property in the urban context. The chapter demonstrates these compactness indicators first by application to theoretical geometric shapes and then a range of English urban areas. The chapter reflects on the interpretation of the core concept of compactness, and suggests additional indicators such as ‘built compactness’ and ‘population compactness’.
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Notes
- 1.
Ironically, that most abstract of disciplines, mathematics uses the case of urban compactness to illustrate the ‘isoperimetric problem’, concerning optimisation of area while minimising perimeter (Ashbaugh and Benguria no date), also referred to as the ‘Queen Dido’ problem, from Virgil’s account in the Aeneid concerning the challenge to build the city of Carthage within the bounds laid out by a strip of oxhide (for example, as discussed by Lord Kelvin 1894).
- 2.
- 3.
This is not to say that we are concerned with all of the ways in which an urban shape does or does not reflect the properties of a circle—for example, a circle has translational and rotational symmetry, and is consistently curved and perfectly convex; but these are properties that no urban area (boundary) has.
- 4.
English Urban Areas, 2001 from Edina UKBorders (https://www.census.ac.uk/search/Full_display.aspx?id=1081) This work is based on data provided with the support of the EPSRC and JISC and uses boundary material which is copyright of the Crown and the ED-LINE Consortium.
- 5.
This is referring to the urban and geographical contexts of properties such as population density, employment density and so on. In physics, of course, density is associated with volume.
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Acknowledgements
This chapter reports on research originally carried out as part of the SOLUTIONS project (Sustainability Of Land Use and Transport In Outer NeighbourhoodS), funded by the UK Engineering and Physical Sciences Research Council (EPRSC).
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Marshall, S., Gong, Y., Green, N. (2019). Urban Compactness: New Geometric Interpretations and Indicators. In: D'Acci, L. (eds) The Mathematics of Urban Morphology. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-12381-9_19
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