# Category: Finite geometry

Incidence structure
In mathematics, an incidence structure is an abstract system consisting of two types of objects and a single relationship between these types of objects. Consider the points and lines of the Euclidean
Hall plane
In mathematics, a Hall plane is a non-Desarguesian projective plane constructed by Marshall Hall Jr. (1943). There are examples of order p2n for every prime p and every positive integer n provided p2n
Fano plane
In finite geometry, the Fano plane (after Gino Fano) is a finite projective plane with the smallest possible number of points and lines: 7 points and 7 lines, with 3 points on every line and 3 lines t
Lam's problem
In finite geometry, Lam's problem is the problem of determining if a finite projective plane of order ten exists.The order ten case is the first theoretically uncertain case, as all smaller orders can
Near polygon
In mathematics, a near polygon is an incidence geometry introduced by Ernest E. Shult and Arthur Yanushka in 1980. Shult and Yanushka showed the connection between the so-called tetrahedrally closed l
Non-Desarguesian plane
In mathematics, a non-Desarguesian plane is a projective plane that does not satisfy Desargues' theorem (named after Girard Desargues), or in other words a plane that is not a Desarguesian plane. The
André plane
In mathematics, André planes are a class of finite translation planes found by André. The Desarguesian plane and the Hall planes are examples of André planes; the two-dimensional regular nearfield pla
Blocking set
In geometry, specifically projective geometry, a blocking set is a set of points in a projective plane that every line intersects and that does not contain an entire line. The concept can be generaliz
Hughes plane
In mathematics, a Hughes plane is one of the non-Desarguesian projective planes found by .There are examples of order p2n for every odd prime p and every positive integer n.
Unital (geometry)
In geometry, a unital is a set of n3 + 1 points arranged into subsets of size n + 1 so that every pair of distinct points of the set are contained in exactly one subset. n ≥ 3 is required by some auth
Galois geometry
Galois geometry (so named after the 19th-century French mathematician Évariste Galois) is the branch of finite geometry that is concerned with algebraic and analytic geometry over a finite field (or G
Finite geometry
A finite geometry is any geometric system that has only a finite number of points.The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry ba
PG(3,2)
In finite geometry, PG(3,2) is the smallest three-dimensional projective space. It can be thought of as an extension of the Fano plane.It has 15 points, 35 lines, and 15 planes. It also has the follow
Combinatorics of Finite Geometries
Combinatorics of Finite Geometries is an undergraduate mathematics textbook on finite geometry by Lynn Batten. It was published by Cambridge University Press in 1986 with a second edition in 1997 (ISB