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incidence geometry
In mathematics, incidence geometry is the study of incidence structures. A geometry such as the Euclidean plane is a complicated object involving concepts such as length, angles, continuity, betweenness and incidence. An ''incidence structure'' is what is obtained when all the other concepts are removed and all that remains is the data about which points lie on which lines. Even with this severe limitation, theorems can be proved and interesting facts emerge concerning this structure. Such fundamental results remain valid when additional concepts are added back to form a richer geometry. It sometimes happens that authors will blur the distinction between a study and the objects of that study, so it is not surprising to find that some authors will refer to incidence structures as incidence geometries.〔As, for example, L. Storme does in his chapter on Finite Geometry in 〕
Incidence structures arise naturally and have been studied in various areas of mathematics. Consequently there are different terminologies used to describe these objects. In graph theory they are called hypergraphs and in combinatorial design theory they are called block designs. Besides the difference in terminology, each area approaches the subject differently and is interested in the types of questions about these objects that are relevant to that discipline. Using geometric language, as is done in incidence geometry, shapes the topics and examples that are normally presented. It is, however, possible to translate the results from one discipline into the terminology of another, but this often leads to awkward and convoluted statements which do not appear to be natural outgrowths of the topics. In the examples selected for this article we will use only those which have a natural geometric flavor.
A special case that has generated much interest deals with finite sets of points in the Euclidean plane and what can be said about the number and types of (straight) lines that are determined by them. Some of the results of this situation can be extended to more general settings since only incidence properties are being considered.
== Incidence structures ==
(詳細はウィキペディア（Wikipedia）』
■ウィキペディアで「incidence geometry」の詳細全文を読む
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