Is the share of a central place in the population of the area, served by this central place, a constant for all levels of the Christaller’s hierarchy?
- Authors: Dmitriev R.V.1,2
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Affiliations:
- Institute of Geography, Russian Academy of Sciences
- Institute for African Studies, Russian Academy of Sciences
- Issue: No 1 (2019)
- Pages: 128-135
- Section: ВЗГЛЯД ГЕОГРАФА
- URL: https://journals.eco-vector.com/2587-5566/article/view/11581
- DOI: https://doi.org/10.31857/S2587-556620191128-135
- ID: 11581
Cite item
Abstract
One of the conditions of the central place theory is the assumption of a constant k parameter – a share of a central place in the population of the area served by this central place – for all levels of the Christaller’s hierarchy. Nevertheless, we did not find a rigorous proof of this assertion (underlying the Beckmann-Parr equation) in the bibliography on the central place theory. If this condition is assumed true, it also remains unclear – whether for all or only for strictly defined k-values. We have established that if the chosen K-value of the Christaller’s hierarchy is constant at every lattice level, the Beckmann-Parr equation holds for all meaningful values of k. At the same time we found that the range of k-values for an ideal Christaller’s lattice is bounded above by not an asymptote at k = 1, but an exact almost twice smaller value equal to K-(K^2-K)^0.5. Since the latter changes very slightly during a radical rearrangement of the lattice from K = 3 to K = 7, we can state that we have discovered the new nonstrict invariant in the central place theory – the maximum value of k.
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About the authors
R. V. Dmitriev
Institute of Geography, Russian Academy of Sciences; Institute for African Studies, Russian Academy of Sciences
Author for correspondence.
Email: dmitrievrv@yandex.ru
Russian Federation, 29, Staromonetny, Moscow, 119017; 30/1, Spiridonovka str., Moscow, 123001
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