Concept
Projective plane
Related concepts (30)
Pappus's hexagon theorem
In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that given one set of collinear points and another set of collinear points then the intersection points of line pairs and and and are collinear, lying on the Pappus line. These three points are the points of intersection of the "opposite" sides of the hexagon . It holds in a projective plane over any field, but fails for projective planes over any noncommutative division ring. Projective planes in which the "theorem" is valid are called pappian planes.
Steiner system
In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ = 1 and t = 2 or (recently) t ≥ 2. A Steiner system with parameters t, k, n, written S(t,k,n), is an n-element set S together with a set of k-element subsets of S (called blocks) with the property that each t-element subset of S is contained in exactly one block. In an alternate notation for block designs, an S(t,k,n) would be a t-(n,k,1) design. This definition is relatively new.
Collineation
In projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to itself, such that the of collinear points are themselves collinear. A collineation is thus an isomorphism between projective spaces, or an automorphism from a projective space to itself. Some authors restrict the definition of collineation to the case where it is an automorphism. The set of all collineations of a space to itself form a group, called the collineation group.
Combinatorial design
Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry. These concepts are not made precise so that a wide range of objects can be thought of as being under the same umbrella. At times this might involve the numerical sizes of set intersections as in block designs, while at other times it could involve the spatial arrangement of entries in an array as in sudoku grids.
Affine plane
In geometry, an affine plane is a two-dimensional affine space. Typical examples of affine planes are Euclidean planes, which are affine planes over the reals equipped with a metric, the Euclidean distance. In other words, an affine plane over the reals is a Euclidean plane in which one has "forgotten" the metric (that is, one does not talk of lengths nor of angle measures).
Girard Desargues
Girard Desargues (ʒiʁaʁ dezaʁɡ; 21 February 1591 - September 1661) was a French mathematician and engineer, who is considered one of the founders of projective geometry. Desargues' theorem, the Desargues graph, and the crater Desargues on the Moon are named in his honour. Born in Lyon, Desargues came from a family devoted to service to the French crown. His father was a royal notary, an investigating commissioner of the Seneschal's court in Lyon (1574), the collector of the tithes on ecclesiastical revenues for the city of Lyon (1583) and for the diocese of Lyon.
Mutually orthogonal Latin squares
In combinatorial mathematics, two Latin squares of the same size (order) are said to be orthogonal if when superimposed the ordered paired entries in the positions are all distinct. A set of Latin squares, all of the same order, all pairs of which are orthogonal is called a set of mutually orthogonal Latin squares. This concept of orthogonality in combinatorics is strongly related to the concept of blocking in statistics, which ensures that independent variables are truly independent with no hidden confounding correlations.
Pencil (geometry)
In geometry, a pencil is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a plane, or the set of circles that pass through two given points in a plane. Although the definition of a pencil is rather vague, the common characteristic is that the pencil is completely determined by any two of its members. Analogously, a set of geometric objects that are determined by any three of its members is called a bundle.
Quasifield
In mathematics, a quasifield is an algebraic structure where and are binary operations on , much like a division ring, but with some weaker conditions. All division rings, and thus all fields, are quasifields. A quasifield is a structure, where and are binary operations on , satisfying these axioms: is a group is a loop, where (left distributivity) has exactly one solution for , Strictly speaking, this is the definition of a left quasifield. A right quasifield is similarly defined, but satisfies right distributivity instead.
Perspectivity
In geometry and in its applications to drawing, a perspectivity is the formation of an image in a picture plane of a scene viewed from a fixed point. The science of graphical perspective uses perspectivities to make realistic images in proper proportion. According to Kirsti Andersen, the first author to describe perspectivity was Leon Alberti in his De Pictura (1435). In English, Brook Taylor presented his Linear Perspective in 1715, where he explained "Perspective is the Art of drawing on a Plane the Appearances of any Figures, by the Rules of Geometry".