Abstract
The topodynamic interpretation of the urban world history stems from a reflection that also gave birth to the topodynamic model, and the Urban Metric System. Altogether, the topodynamic theory, the topodynamic model, and the Urban Metric System originate from the Fermat, Weber, and attraction–repulsion problems; the topodynamic theory and the Urban Metric System both use vector field analysis. The originality of the topodynamic model is the fact that it is not econometric, despite it being fundamentally economic. It produces reliable demo-economic projections in a context where general equilibrium is not looked for or assumed to be the natural guide of economic evolution. As for the Urban Metric System, it is conceived to fill the major gap of the absence of a mathematical method to delimit urban areas (central cities, central agglomerations, metropolitan areas, etc.). Its only input is the disaggregated spatial distribution of population, and its outputs are the centers and boundaries of the various urban areas.
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That solution was direct and trigonometric. In 1992, Pey-Chun Chen, Pierre Hansen, Brigitte Jaumard, and Hoang Tuy developed an algorithm to solve the general attraction–repulsion problem involving more than three reference points. Finally, in 2013, Tellier has found a direct geometrical solution to the triangle attraction–repulsion problem (published in 2014).
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Sortia et al. (1987).
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Tellier and Gelb (2018). The following pages are essentially based on that article.
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Tellier, LN. (2019). The Topodynamic Model: Origin and Fallouts. In: Urban World History. Springer, Cham. https://doi.org/10.1007/978-3-030-24842-0_15
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DOI: https://doi.org/10.1007/978-3-030-24842-0_15
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