Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-06-06T06:51:44.337Z Has data issue: false hasContentIssue false
  • English
  • Français

Population in cities

Published online by Cambridge University Press:  22 September 2016

C. W. Kilmister
C. W. Kilmister*
Affiliation:
King’s College, London WC2R 2LS
Get access Rights & Permissions [Opens in a new window]

Extract

I want to deal with one piece of applied mathematics which is a good example of the way in which—in nearly all applications of mathematics—the important steps are those of tentative model-building, and the testing of such models against reality. It is this feature that makes mechanics such an atypical case; there the model, Newton’s laws, is made for one beforehand. In the present instance the initial problem, whose partial solution leads, as usual, to other problems, can be stated very simply: in most cities the population density, σ, tends to fall off with distance, r, from the centre.

Type
Research Article
Information
The Mathematical Gazette , Volume 60 , Issue 411 , March 1976 , pp. 11 - 24
Copyright
Copyright © Mathematical Association 1976

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Stewart, J. Q., An inverse distance relation for certain social influences, Science, N. Y. 93, 89 (1941).Google Scholar
2. Stewart, J. Q., Empirical and mathematical rules concerning the distribution of population, Geogrl Rev. 47, 461 (1947).Google Scholar
3. Stewart, J. Q., Suggested principles of ’social physics’, Science, N. Y. 106, 179 (1947).Google Scholar
4. Wilson, A. G., Entropy in urban and regional modelling (London, 1970).Google Scholar
5. Gurevich, B. L. and Saushkin, Y. G., The mathematical method in geography, Soviet Geogr. I (Part 4), 3 (1966).Google Scholar
6. Ajo, R., Acta geogr. (1965).Google Scholar
7. Bussiere, R. and Snickars, F., Derivation of the negative exponential model by an entropy maximising method, Environ. and Plan. 2, 295 (1970).Google Scholar
8. Amson, J., The dependence of population distribution on location costs, Environ, and Plan. 4, 163 (1972).Google Scholar
9. Amson, J., Equilibrium models of cities: 1. An axiomatic theory, Environ. and Plan. 4, 429 (1972).Google Scholar
10. Amson, J., Equilibrium models of cities: 2. Single species cities, Environ. and Plan. 5, 295 (1973).Google Scholar
ll. Amson, J., Equilibrium and catastrophic modes of urban growth, London Papers in Regional Science 4 (1973).Google Scholar
12. Wicksteed, P., Economic Journal (June 1894).Google Scholar
13. Heathfield, D. F., Production functions. Macmillan (1971).CrossRefGoogle Scholar
14. Lane, J. Homer, On the theoretical temperature of the Sun, Amer. Jour. of Sci. and Arts 4, 57(1870).Google Scholar
15. Emden, R., Gaskugeln. Teubner (Leipzig, 1907).Google Scholar
16. Eddington, A. S., The internal constitution of the stars. Cambridge University Press (1926).Google Scholar
17. Thorn, R., Stabilité structurelle et morphogénèse. Benjamin (1973). (This is now available in English as Structural stability and morphogenesis, same publisher (1975) and the passage referred to is on pp. 62-63.)Google Scholar
18. Woodcock, A. and Poston, T., A geometrical study of the elementary catastrophes. Springer (1974).Google Scholar
19. (a) In words: (Zeeman, E. C., The geometry of catastrophe, Times Literary Supplement 3641, 1566 (Dec. 10, 1971).Google Scholar
(b) For mathematicians: Brocker, Th. (trans. Lander, L.), Differentiable germs and catastrophes. Cambridge University Press (1975).Google Scholar