Incidence

Incidence is the relation of containment or meeting between geometric objects, such as a point lying on a line or two curves intersecting.

Incidence structure: A system of points and other objects together with a specified relation describing which objects are incident. This general framework packages geometric objects and their incidence relations.
Incidence theorem: A mathematical result bounding or characterizing the number of incidences among specified geometric objects. Such theorems turn a relation into quantitative limits.
Discrete geometry: The study of finite or discrete geometric configurations and their combinatorial properties. Incidence is one of its central ways to measure configuration complexity.
Intersection: The set of elements common to two or more sets, or the place where geometric objects meet. Intersection describes shared points; incidence can also express containment without two objects crossing.
Point-line geometry: A geometry whose basic objects are points and lines, connected by an incidence relation. It gives the simplest setting for point-on-line incidence.
Szemerédi–Trotter theorem: A theorem bounding incidences between a finite set of points and a finite set of lines in the plane. It gives a sharp general bound for point-line incidences.
Additive combinatorics: The study of additive structure in sets using combinatorial and analytic methods. Incidence bounds can control solutions to equations involving sums and products.
Containment: The relation in which one set or geometric object is entirely included in another. Containment is one form of incidence, but incidence also includes objects meeting at a point.
Incidence matrix: A matrix recording which pairs of objects in two sets are related. Its entries encode incidences between two classes of geometric objects.
Bézout's theorem: A theorem stating that plane algebraic curves of degrees m and n have at most mn intersections, counting multiplicity, when they share no component. It bounds intersections by the algebraic degrees of the curves.

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