Theory of the central places of V. Kristaller and A. Lyosha
The development of this theory is connected with the names of the German scientists Walter Kristaller and Augusta Lesha. In 1933, The work of Kristaller Central places in Southern Germany was published. It revealed the spatial patterns of the location of cities, knowledge of which is necessary to improve the territorial organization of society and improve the administrative-territorial division of Germany. central place means a large city, a center for all other localities in the area, providing them with the main goods and services. The smallest cells of the settlement are investigated, which, as Kristaller admits, exist perfectly evenly and form regular triangular networks. He wrote: "I connected on the map with straight lines of the city of identical sizes ... At the same time the map was filled with triangles, often isosceles; The distances between cities of the same size were approximately equal and formed hexagons. I found that small towns in South Germany are very often and very accurately located at a distance of 21 km from each other ... I first of all created, as they say, an abstract economic model, although in reality it can not be found anywhere in pure form. Mountains, differences in soils, different population density, historical development and political factors introduce deviations into these models. "
Given a uniform distribution of the population, the sales areas that have the shape of regular hexagons are evenly distributed (see Figure 8.4), which ensures the smallest average distance for buyers to travel to the shopping center. Any center always has an equal number of settlements ( k ), which occupy a lower hierarchical level. As an example, consider the case where the hierarchical series includes cities, towns and villages with k - 7. Around each city will be located 6 villages (7th - the city itself), and around each village - 6 villages. As a result, around the highest (in this case) degree of hierarchy - the city - there will be 6 villages and 36 villages. From these provisions, V. Kristaller concludes that the hierarchy system from one step to the next corresponds to a correct geometric progression. For example, with k = 8, there should be 7 settlements in the sphere of influence of each village, 49 settlements in the sphere of influence of each village, 343 settlements in the sphere of influence of each city.
Fig. 8.4. Market Zones (according to W. Kristaller)
To explain the formation of different levels of services, Kristaller introduces the concept of "the radius of the implementation of services and products", which will be different for market zones of different hierarchies. For example, primary education can be obtained in the village; for secondary education it is necessary to study at a school located in a settlement; in order to get a secondary special education, one must study in the village; graduate higher education is possible only in the city. However, as you move up the ladder of education, the number of training centers decreases, and the number of students increases. V. Kristaller concludes that there is a lower limit beyond which the inflow of consumers is too small to justify the activities of the enterprise. If, for example, the lower limit for this activity is 34 for k = 7, then enterprises of this type can be located not in villages, but in settlements and larger settlements.
Q. The crystal sets three possible options for determining the dimensions of k.
1. Sales Orientation If the source of supply of goods or the provision of services produced in central locations must be at a minimum distance from dependent locations, then the hierarchy k = 3, since in this case the number of central locations is maximized and the links exist only with two of the nearest points (the third is the center itself), which leads to a symmetric cluster hierarchy.
2. Transport Orientation For large transport costs, the k = hierarchy is appropriate, since the largest number of central locations will be located on the same route connecting the larger cities, which provides the lowest costs for the construction and operation of roads. Thus communications will be established only with three of six dependent places that will give other scheme of nesting.
3. Administrative orientation. For the implementation of clear administrative control, according to V. Kristaller, a hierarchy based on k = 7, in which the central place is associated with all six nearest dependent places.
As a result of the study, V. Kristaller identified a number of spatial patterns.
1. The group of identical central places has hexagonal complementary areas (ie territories serviced by central locations), and the central places themselves form the right triangular lattice. This ensures optimal movement of consumers of goods and services, optimization of market, transport infrastructures and administrative device.
2. The ideal location of settlements can exist only on an abstract territory - a homogeneous plain with the same density and purchasing power of the population, a uniform distribution of resources, the same transport connection. It is also assumed that the purchase and provision of central goods and services are carried out only in the nearest central place and not one of the central places does not receive additional profit.
V. Kristaller's work was subjected to numerous criticisms, connected with the fact that nowhere on the Earth does not exist an ideal hexagonal (hexagonal) lattice. However, its construction is of great importance for comparison of real and abstract models of settlements, which allows predicting future changes in the settlement system. They are also necessary for solving practical problems of the geography of the non-productive sphere.
The development of the theory of central places was the work of A. Lyosha, which presents a more complex model for locating settlements, as close to reality as possible. A. Lyosch believes that as the transport costs increase, the prices of goods and services in the peripheral parts of the market zones increase, and demand falls. As a result, the cone of demand - the radius of the zone for the sale of goods and services of central places, the lower limit of which is determined by the threshold value of the market, the upper one by the distance to which it is expedient to sell the product (Figure 8.5). With the help of calculations A. Lyosch proves that with the total division of the territory into market zones and the direct demand line ( PF ), the total volume of demand cones is maximal when their bases have a hexagonal shape.
Fig. 8.5. The cone of demand with a hexagonal base (according to A. Lyosha) :
PQ - the amount of demand in the center of the market zone; PF - the direction of lower demand and higher prices; FQ - distance to the central place
Achieving the coincidence of the maximum possible number of centers with k = 3, k = 4, k = 7 thus optimizing the market, transport and administrative structures), A.Losch rotates superimposed market zones of different sizes around the central place. Rotated areas he refers to as "economic landscapes". As a result, 6 sectors of the "rich" and 6 "poor" settlements. With this arrangement, according to A. Lyosha, the total distance between the settlements is minimized, and the range of goods and services that can be purchased on-site is expanding. At the same time, within the sectors with a large number of settlements, their size increases with distance from the main city, and small settlements are located approximately halfway between the two larger ones.
The A.Liesch model, in comparison with V.Kristaller's constructions, is more flexible, assuming that the values k can freely vary. From this it follows that the central places form an almost continuous sequence of centers, and not a strict vertical hierarchy, as in V. Kristaller. Therefore, settlements of a higher rank do not necessarily fulfill all the functions characteristic of places of lower rank, and settlements with an equal number of functions do not always perform the same functions.
Despite the well-known abstractness of the constructions of W. Kristaller and A. Lyosha, their works played a big role in the development of the theoretical and methodological foundations of modern geography. As noted by Yu. G. Saushkin, the main merit of these authors is to try to open the law of mutual spatial distribution of settlements and, having learned the objective law, apply it in newly developed territories. By this they opened the way to the study of territorial systems of the population and the non-productive sphere and promoted the wide application of mathematical methods in economic and social geography.
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