An Introduction to Incidence Geometry

An Introduction to Incidence Geometry
Author: Bart De Bruyn
Publisher: Birkhäuser
Total Pages: 380
Release: 2016-11-09
Genre: Mathematics
ISBN: 3319438115

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This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end of the book. This book is aimed at graduate students and researchers in the fields of combinatorics and incidence geometry.

Handbook of Incidence Geometry

Handbook of Incidence Geometry
Author: Francis Buekenhout
Publisher: North-Holland
Total Pages: 1440
Release: 1995
Genre: Mathematics
ISBN:

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Hardbound. This Handbook deals with the foundations of incidence geometry, in relationship with division rings, rings, algebras, lattices, groups, topology, graphs, logic and its autonomous development from various viewpoints. Projective and affine geometry are covered in various ways. Major classes of rank 2 geometries such as generalized polygons and partial geometries are surveyed extensively.More than half of the book is devoted to buildings at various levels of generality, including a detailed and original introduction to the subject, a broad study of characterizations in terms of points and lines, applications to algebraic groups, extensions to topological geometry, a survey of results on diagram geometries and nearby generalizations such as matroids.

Foundations of Incidence Geometry

Foundations of Incidence Geometry
Author: Johannes Ueberberg
Publisher: Springer Science & Business Media
Total Pages: 259
Release: 2011-08-26
Genre: Mathematics
ISBN: 3642209726

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Incidence geometry is a central part of modern mathematics that has an impressive tradition. The main topics of incidence geometry are projective and affine geometry and, in more recent times, the theory of buildings and polar spaces. Embedded into the modern view of diagram geometry, projective and affine geometry including the fundamental theorems, polar geometry including the Theorem of Buekenhout-Shult and the classification of quadratic sets are presented in this volume. Incidence geometry is developed along the lines of the fascinating work of Jacques Tits and Francis Buekenhout. The book is a clear and comprehensible introduction into a wonderful piece of mathematics. More than 200 figures make even complicated proofs accessible to the reader.

Projective Geometry

Projective Geometry
Author: Rey Casse
Publisher: OUP Oxford
Total Pages: 212
Release: 2006-08-03
Genre: Mathematics
ISBN: 0191538361

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This lucid and accessible text provides an introductory guide to projective geometry, an area of mathematics concerned with the properties and invariants of geometric figures under projection. Including numerous worked examples and exercises throughout, the book covers axiomatic geometry, field planes and PG(r, F), coordinatising a projective plane, non-Desarguesian planes, conics and quadrics in PG(3, F). Assuming familiarity with linear algebra, elementary group theory, partial differentiation and finite fields, as well as some elementary coordinate geometry, this text is ideal for 3rd and 4th year mathematics undergraduates.

Polynomial Methods and Incidence Theory

Polynomial Methods and Incidence Theory
Author: Adam Sheffer
Publisher: Cambridge University Press
Total Pages: 263
Release: 2022-03-24
Genre: Mathematics
ISBN: 1108832490

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A thorough yet accessible introduction to the mathematical breakthroughs achieved by using new polynomial methods in the past decade.

Foundations of Geometry

Foundations of Geometry
Author: Karol Borsuk
Publisher: Courier Dover Publications
Total Pages: 465
Release: 2018-11-14
Genre: Mathematics
ISBN: 0486828093

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In Part One of this comprehensive and frequently cited treatment, the authors develop Euclidean and Bolyai-Lobachevskian geometry on the basis of an axiom system due, in principle, to the work of David Hilbert. Part Two develops projective geometry in much the same way. An Introduction provides background on topological space, analytic geometry, and other relevant topics, and rigorous proofs appear throughout the text. Topics covered by Part One include axioms of incidence and order, axioms of congruence, the axiom of continuity, models of absolute geometry, and Euclidean geometry, culminating in the treatment of Bolyai-Lobachevskian geometry. Part Two examines axioms of incidents and order and the axiom of continuity, concluding with an exploration of models of projective geometry.

Projective Geometry

Projective Geometry
Author: Albrecht Beutelspacher
Publisher: Cambridge University Press
Total Pages: 272
Release: 1998-01-29
Genre: Mathematics
ISBN: 9780521483643

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Projective geometry is not only a jewel of mathematics, but has also many applications in modern information and communication science. This book presents the foundations of classical projective and affine geometry as well as its important applications in coding theory and cryptography. It also could serve as a first acquaintance with diagram geometry. Written in clear and contemporary language with an entertaining style and around 200 exercises, examples and hints, this book is ideally suited to be used as a textbook for study in the classroom or on its own.

Perspectives on Projective Geometry

Perspectives on Projective Geometry
Author: Jürgen Richter-Gebert
Publisher: Springer Science & Business Media
Total Pages: 573
Release: 2011-02-04
Genre: Mathematics
ISBN: 3642172865

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Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.

Foundations of Three-Dimensional Euclidean Geometry

Foundations of Three-Dimensional Euclidean Geometry
Author: Izu Vaisman
Publisher: CRC Press
Total Pages: 287
Release: 2020-11-25
Genre: Mathematics
ISBN: 1000110494

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This book presents to the reader a modern axiomatic construction of three-dimensional Euclidean geometry in a rigorous and accessible form. It is helpful for high school teachers who are interested in the modernization of the teaching of geometry.