GEOGRAPHY AND THE PROPERTIES OF SURFACES. HOMOLOGICAL TRANSFORMATIONS IN FOUR-DIMENSIONAL SPACE.

摘要

The development of geometrical methods applicable to problems in geography and regional planning requires the detailed study of the theoretical foundation upon which those methods are based. This is the obvious requirement for any scientific investigation where theory,research (development of the methodology),and application are discussed in that order. The paper deals with one of such methods,namely,the study of the homological transformations in a plane in four-dimensional space. The theoretical foundation is the four-dimensional descriptive geometry. A brief discussion is made introducing three of the most important methods of representation. Complementing the study,three problems of practical value are presented,pointing out that their solutions depend on the use of the methodology introduced in the paper. (Author)