Projective plane

Projective plane

A projective plane is a geometric structure that is obtained by augmenting the ordinary plane with points at infinity. It consists of a set of points and a set of lines, where each line is defined as a subset of the set of points. The defining property of a projective plane is that for any two distinct points, there is exactly one line that includes both points. Conversely, a projective plane can be obtained from an affine plane by adding an extra point to each line (a point at infinity), and connecting these points by a line.From: Cone Beam Computed Tomography [2019], Applying combinatorics in the design of multiversion exams [2023], Coding and Signal Processing for Magnetic Recording Systems [2019]

An Introduction to Error-Correcting Codes

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Published in Erozan M. Kurtas, Bane Vasic, Advanced Error Control Techniques for Data Storage Systems, 2018

Mario Blaum

x0=0. Conversely, a projective plane can be obtained from an affine plane by adding an extra point to each line (a point at infinity), and connecting these points by a line. Figure 14.2 illustrates this idea for a geometry with nine points. Each line in the projective geometry contains one more point, and the points at infinity ∞1,∞2,∞3,∞4 create a line so that no parallel classes exist.

Discrete Mathematics

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Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018

Dan Zwillinger

A finite projective plane is a finite set of points together with subsets of points called lines that satisfy the axioms:Any two points are on exactly one line.Any two lines intersect in exactly one point.There are four points, no three of which are collinear.

Applying combinatorics in the design of multiversion exams

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Journal Information

Published in International Journal of Mathematical Education in Science and Technology, 2023

Jila Niknejad, Margaret Bayer

A projective plane consists of a set of points and a set of lines, each line defined as a subset of the set of points, having the following properties: For any two distinct points, there is exactly one line that includes both points.For any two distinct lines, there is exactly one point that is included in both lines.There are four points such that no line includes more than two of them.

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An Introduction to Error-Correcting Codes

Discrete Mathematics

Applying combinatorics in the design of multiversion exams