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Incidence geometry

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collinearity
In geometry, collinearity of a set of points is the property of their lying on a single line. A set of points with this property is said to be collinear (sometimes spelled as colinear). In greater generality, the term has been used for aligned objects, that is, things being "in a line" or "in a row".
Problem of Apollonius
construct circles that are tangent to three given circles in a plane
projective plane
geometric concept of a 2D space with a "point at infinity" adjoined
Bézout's theorem
theorem calculating the number of intersection points of two algebraic curves in terms of their degrees
concyclic points
a set of points that lie on a single circle
Fano plane
finite projective plane of order 2
incidence geometry
the mathematical study of incidence structures
incidence structure
an abstract mathematical object generalizing the properties of points and lines in the Euclidean plane
De Bruijn–Erdős theorem
incidence geometry theorem
Moulton plane
non-desarguesian plane geometry
abstract polytope
algebraic partially ordered set or poset which captures the combinatorial properties of a traditional polytope, but not any purely geometric properties such as angles, edge lengths, etc
flag
sequence of faces of a polytope
generalized quadrangle
type of incidence structure in mathematics
Möbius plane
particular kind of plane geometry, built upon some affine planes by adding one point
generalized polygon
generalised concept of incidence structure of polygons
mutually unbiased bases
a set of orthonormal bases, where each vector of a given basis has the same overlap with all the vectors of other bases
linear space
basic structure in incidence geometry