Results 141 to 150 of about 236,638 (182)

On the foundations of incidence geometry

Geometriae Dedicata, 1988
Diagram geometries and chamber systems of various types have been used and investigated intensively in recent years - not only in finite group theory, but in other areas as well. This development has led to a need for some clarification of the variations and generalizations introduced by the many authors, and for a discussion of the different axiomatic
Buekenhout, Francis, Buset, Dominique
exaly   +4 more sources

On finite models of Hilbert's incidence geometry

Discrete Mathematics
In this paper, the authors give a lower bound on the number of such models with \({n}\) points using finite models of the first group of Hilbert's axioms of Euclidean geometry (denote with \(A\)). By \(\mathrm{HilbInc}(n)\), the authors denote the number of nonisomorphic models of \(A\) with the point set \({1, 2,\dots,n}\) and calculate the exact ...
Kristina Ago, Bojan Basic, Milica Maksimovic, Milica Sobot   +3 more
exaly   +4 more sources

Modal logics for incidence geometries

Journal of Logic and Computation, 1997
Let \(S=(P,L,\text{in})\) be an incidence plane by the well-known axioms: \(P,L\neq\emptyset\); \(\text{in}\subseteq P\times L\); \(P\cap L=\emptyset\); two points are together incident with one and only one line; each line contains at least two different points; each point belongs at least to two different lines.
Philippe Balbiani, Luis Fariñas del Cerro, Tinko Tinchev, Dimiter Vakarelov   +3 more
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On the Incidence Geometry of Grassmann Spaces

Geometriae Dedicata, 1999
The main result is a characterization of the Grassmann space \({\mathbf G}\) of a projective space \(\mathcal P\). By definition, the point set \(P\) of \({\mathbf G}\) is the set of lines of \(\mathcal P\), the line set \(\mathcal L\) of \({\mathbf G}\) consists of all plane line pencils in \(\mathcal P\).
FERRARA DENTICE, Eva, MELONE N.
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Incidence and Metric Geometry

1981
In this section we shall define the notions of an abstract geometry and an incidence geometry. These are given by listing a set of axioms that must be satisfied. After the definitions are made, we will give a number of examples which will serve as models for these geometries.
Richard S. Millman, George D. Parker
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FORMALIZATION OF HILBERT'S GEOMETRY OF INCIDENCE AND PARALLELISM

Synthese, 1997
The author first describes how \textit{D. Hilbert} changed the phrasing of his axioms of incidence in the various early editions of his Grundlagen der Geometrie [(Teubner, Leipzig) (1899; JFM 30.0424.01); second edition (1903; JFM 34.0523.01); seventh edition (1930; JFM 56.0481.01)], in which ``bestimmen'' gave way to ``es gibt''.
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Geometric Hyperplanes of Lie Incidence Geometries

Geometriae Dedicata, 1997
Let \(\Gamma=({\mathcal P},{\mathcal L})\) be a geometry of points and lines. A subspace of \(\Gamma\) is a set of points which contains every line that meets it in at least two points. An embedding \(\mu\) of \(\Gamma\) in a finite-dimensional vector space \(V\) consists of a map \(\mu_1\) of \({\mathcal P}\) into the set of 1-subspaces of \(V\) and a
Cooperstein, Bruce N., Shult, Ernest E.
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Incidence loops and their geometry

1992
Publisher Summary This chapter discusses the concept of incidence loops and their geometry. An incidence group (P, L,·) is a group (P,·) together with a structure (P, L) of an incidence space such that both structures are compatible. The notion of incidence group can be generalized by weakening the assumptions concerning the algebraic structure of P;
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On apartments in incidence geometry

2009
info:eu-repo/semantics ...
Buekenhout, Francis, Leemans, Dimitri
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Preliminaries and Incidence Geometry (I)

2015
This chapter contains a brief summary of several types of mathematical knowledge needed to read this book, including the elements of logic, set theory, mapping theory, and algebraic structures such as number systems and vector spaces. Definitions of basis, dimension, linear mappings, isomorphism, matrices and determinants are given; there is also ...
Edward John Specht, Harold Trainer Jones, Keith G. Calkins, Donald H. Rhoads   +3 more
openaire   +1 more source