Mathematical Elements of Maps

Abstract

Mathematical elements of maps comprise cartographic projections, map scale and map borders. Cartographic projection is the mathematical possibility to represent the spherical surface of Earth on a flat surface, that is, a map, in a given scale. It is a separate issue in cartography, but here in topography, apart from the concept and classification of cartographic projections, the Gauss–Krüger projection and the UTM-projection are separately and purposely presented as the most widely used in the production of large-scale maps in the world. The scale of maps as a ratio between distances on a map and those very distances in nature is more extensively elaborated both regarding its substance and regarding its labeling as a numerical and graphical scale and as a significant category of map measurement. Also presented are the features of a surface scale, as well as the ways of measuring surface size on maps and in nature. The map border is presented as an element for recognizing the mathematical elements of maps in a way that presents map border features through examining the types of map borders, content in map borders (inter-border and extra border) and properties of enclosed map borders. The point is to become acquainted with the basics of design, but even more so to become familiar with the possibilities to read and set coordinates, map measurements, and so on.