Abstract
This chapter introduces incidence geometry. Incidence geometry arises from the points, lines, and planes of elementary geometry, based on properties stated in terms of inclusion and intersection. An example of such a property is the fact that two distinct points are elements of (are incident with) a unique line. The subject generalizes in various directions with various degrees of abstraction. As in many other mathematical subjects, the incidence may be somehow compatible with more structure. This leads in particular to ordered (incidence) geometry based on the properties related to segments of lines, half-lines, half-planes and half-spaces in elementary geometry, to topological (incidence) geometry when closed and open subsets of elementary geometry are taken into account and to metric (incidence) geometry based on the additional structure provided by perpendicularity, distance and motion.
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