Modern Trends of Mathematical Application in Geographical Thoughts and Its Environment - Increasing Relevance in Geo-scientific Study

A number of ways in which mathematics is used in geography are mentioned. Plane Euclidean geometry is used in surveying small areas in the field, while spherical geometry and trigonometry are required in the construction of map projections, both traditional elements of mathematical geography. In the newer applications of mathematics to geography, topology is being used increasingly in the spatial analysis of networks. Graph theory provides indices to describe various types of network, such as drainage patterns. Differential equations are needed to study dynamic processes in geomorphology. Statistical techniques, such as trend surface analysis, factor analysis, cluster analysis and multiple discriminant analysis, can be applied to the description and analysis of the data of regional geography. Mathematical models are used in various forms to simplify the problems in geography. Examples of analogue models, such as the gravity model, are mentioned. Simulation models and Markov chain stochastic models are of value in studying certain geographical processes. Game theory is mentioned briefly. In the final section planning and prediction are very briefly referred to. In the former linear programming is a useful method, and in the latter trend fitting and extrapolation are applicable. Geography has gained a great deal in quantitative value and precision in adopting mathematical techniques (Cuchlaine A. M. King, 2006).