GEOMETRIC PROBLEMS IN URBANISM
Authors: Habrel M. 
Published: May 2021

The article considers the phenomenon of urban geometry and the essence of geometric problems in urban planning. The proposed approach corresponds to the generally accepted understanding of cities through knowledge of the arts, humanities, social sciences and engineering. Geometry expands the understanding of cities and processes in them both in the historical context and in modern realities and conditions. The definiteness of the geometric dimension in the problems of spatial organization and development of urbanized systems is confirmed.
Professional consideration and use of geometric indicators and properties is a condition for increasing the validity of architectural and urban planning decisions. The geometry of the functional city was based on ideas and solutions that focused on process control. The geometry of the space of today's city, according to the author, should stimulate its development by analogy with a living organism. Historical analysis expands the idea of the geometry of the city and its spatial implementation. The characteristics of the geometric measurement of different periods allowed us to conclude that the principles of geometry apply to cities of any time and any culture, are associated with the patterns of urban growth. Urban forms change depending on the scale: increasing the scale of the city to hypercomplex urban systems, the organic analogy grows, pure geometric planning is preserved on a local scale.
The theoretical provisions of urban geometry, geometric problems and methods of their solution are substantiated. Identified dichotomies are important for understanding, researching and designing the development of urban systems. They are useful for generalizing different worldviews of space, time and urban geometry: the opposition of the concepts of simplicity and complexity; division and integrity; continuous and intermittent; homogeneity and heterogeneity of the system; certainty and uncertainty. New paradigms and thinking of the city as a hypercomplex system of organic complexity are covered. Geometry determines complexity, scale and shape. Views on space and geometry on the scale of human history have been studied. An attempt is made to understand the "reality" of development and spatial organization of cities. Geometry is used to display order and regularity, as well as in solving urban problems of today. The article highlights, structures and reveals the role of geometry and geometric problems in urban systems, their relationship with other dimensions and problems of spatial organization and urban development.
In the model of multidimensional urban space "human - functions - conditions - geometry - time", which was substantiated by the author to solve problems of urban planning (spatial organization and development of urban systems) a special role is given to the geometric dimension, which is described in detail in the article. It includes many characteristics and indicators: size, configuration, shape, concentration of elements, as well as properties related to scale, intrasystem connections and location in the environment. The importance of urban geometry is illustrated using the author's model of multidimensional urban space on the example of geometric problems of Lviv, in particular placement, relocation and division. The solution of the communication and transport problem in the city is characterized and substantiated taking into account the requirements of the new geometry.