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2. Linear space (geometry) - Wikipedia

   en.wikipedia.org/wiki/Linear_space_(geometry)

   Let L = (P, G, I) be an incidence structure, for which the elements of P are called points and the elements of G are called lines. L is a linear space if the following three axioms hold: (L1) two distinct points are incident with exactly one line. (L2) every line is incident to at least two distinct points. (L3) L contains at least two distinct ...

3. Incidence structure - Wikipedia

   en.wikipedia.org/wiki/Incidence_structure

   Example 1: points and lines of the Euclidean plane (top) Example 2: points and circles (middle), Example 3: finite incidence structure defined by an incidence matrix (bottom) In mathematics, an incidence structure is an abstract system consisting of two types of objects and a single relationship between these types of objects.

4. Pappus configuration - Wikipedia

   en.wikipedia.org/wiki/Pappus_configuration

   The Pappus graph. The Levi graph of the Pappus configuration is known as the Pappus graph.It is a bipartite symmetric cubic graph with 18 vertices and 27 edges. [3]Adding three more parallel lines to the Pappus configuration, through each triple of points that are not already connected by lines of the configuration, produces the Hesse configuration.

5. Configuration (geometry) - Wikipedia

   en.wikipedia.org/wiki/Configuration_(geometry)

   Configurations (4 3 6 2) (a complete quadrangle, at left) and (6 2 4 3) (a complete quadrilateral, at right).. In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.

6. Locus (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Locus_(mathematics)

   Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.

7. Incidence (geometry) - Wikipedia

   en.wikipedia.org/wiki/Incidence_(geometry)

   Lines that meet at the same point are said to be concurrent. The set of all lines in a plane incident with the same point is called a pencil of lines centered at that point. The computation of the intersection of two lines shows that the entire pencil of lines centered at a point is determined by any two of the lines that intersect at that point.