The Geometry Of Incidence

Author : Bart De Bruyn
Publisher : Birkhäuser
Page : 372 pages
File Size : 40,8 Mb
Release : 2016-11-09
Category : Mathematics
ISBN : 9783319438115

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An Introduction to Incidence Geometry by Bart De Bruyn Pdf

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.

Author : Johannes Ueberberg
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 41,9 Mb
Release : 2011-08-26
Category : Mathematics
ISBN : 9783642209727

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Foundations of Incidence Geometry by Johannes Ueberberg Pdf

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.

Author : Harold Laird Dorwart
Publisher : Unknown
Page : 184 pages
File Size : 54,5 Mb
Release : 1966
Category : Mathematics
ISBN : UOM:39015017337414

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The Geometry of Incidence by Harold Laird Dorwart Pdf

Author : Francis Buekenhout
Publisher : North-Holland
Page : 1440 pages
File Size : 53,5 Mb
Release : 1995
Category : Mathematics
ISBN : UOM:39015033341747

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Handbook of Incidence Geometry by Francis Buekenhout Pdf

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.

Author : Harold L. Dorwart
Publisher : Unknown
Page : 159 pages
File Size : 55,8 Mb
Release : 1974
Category : Electronic
ISBN : OCLC:917221044

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The Geometry of Incidence by Harold L. Dorwart Pdf

Author : Albrecht Beutelspacher,Ute Rosenbaum
Publisher : Cambridge University Press
Page : 272 pages
File Size : 53,6 Mb
Release : 1998-01-29
Category : Mathematics
ISBN : 0521483646

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Projective Geometry by Albrecht Beutelspacher,Ute Rosenbaum Pdf

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.

Author : A. Heyting
Publisher : Elsevier
Page : 161 pages
File Size : 46,9 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483259314

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Axiomatic Projective Geometry by A. Heyting Pdf

Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume V: Axiomatic Projective Geometry, Second Edition focuses on the principles, operations, and theorems in axiomatic projective geometry, including set theory, incidence propositions, collineations, axioms, and coordinates. The publication first elaborates on the axiomatic method, notions from set theory and algebra, analytic projective geometry, and incidence propositions and coordinates in the plane. Discussions focus on ternary fields attached to a given projective plane, homogeneous coordinates, ternary field and axiom system, projectivities between lines, Desargues' proposition, and collineations. The book takes a look at incidence propositions and coordinates in space. Topics include coordinates of a point, equation of a plane, geometry over a given division ring, trivial axioms and propositions, sixteen points proposition, and homogeneous coordinates. The text examines the fundamental proposition of projective geometry and order, including cyclic order of the projective line, order and coordinates, geometry over an ordered ternary field, cyclically ordered sets, and fundamental proposition. The manuscript is a valuable source of data for mathematicians and researchers interested in axiomatic projective geometry.

Author : Adam Sheffer
Publisher : Cambridge University Press
Page : 263 pages
File Size : 48,6 Mb
Release : 2022-03-24
Category : Mathematics
ISBN : 9781108832496

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Polynomial Methods and Incidence Theory by Adam Sheffer Pdf

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

Author : Jürgen Richter-Gebert
Publisher : Springer Science & Business Media
Page : 573 pages
File Size : 42,6 Mb
Release : 2011-02-04
Category : Mathematics
ISBN : 9783642172861

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Perspectives on Projective Geometry by Jürgen Richter-Gebert Pdf

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.

Author : Reinhard Klette,Azriel Rosenfeld
Publisher : Elsevier
Page : 675 pages
File Size : 44,9 Mb
Release : 2004-09-04
Category : Computers
ISBN : 9780080477268

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Digital Geometry by Reinhard Klette,Azriel Rosenfeld Pdf

Digital geometry is about deriving geometric information from digital pictures. The field emerged from its mathematical roots some forty-years ago through work in computer-based imaging, and it is used today in many fields, such as digital image processing and analysis (with applications in medical imaging, pattern recognition, and robotics) and of course computer graphics. Digital Geometry is the first book to detail the concepts, algorithms, and practices of the discipline. This comphrehensive text and reference provides an introduction to the mathematical foundations of digital geometry, some of which date back to ancient times, and also discusses the key processes involved, such as geometric algorithms as well as operations on pictures. *A comprehensive text and reference written by pioneers in digital geometry, image processing and analysis, and computer vision*Provides a collection of state-of-the-art algorithms for a wide variety of geometrical picture analysis tasks, including extracting data from digital images and making geometric measurements on the data*Includes exercises, examples, and references to related or more advanced work

Author : Ernest E. Shult
Publisher : Springer Science & Business Media
Page : 682 pages
File Size : 46,5 Mb
Release : 2010-12-13
Category : Mathematics
ISBN : 9783642156274

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Points and Lines by Ernest E. Shult Pdf

The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphic images of them) are characterized in this book by simple local axioms on points and lines. Simple point-line characterizations of Lie incidence geometries allow one to recognize Lie incidence geometries and their automorphism groups. These tools could be useful in shortening the enormously lengthy classification of finite simple groups. Similarly, recognizing ruled manifolds by axioms on light trajectories offers a way for a physicist to recognize the action of a Lie group in a context where it is not clear what Hamiltonians or Casimir operators are involved. The presentation is self-contained in the sense that proofs proceed step-by-step from elementary first principals without further appeal to outside results. Several chapters have new heretofore unpublished research results. On the other hand, certain groups of chapters would make good graduate courses. All but one chapter provide exercises for either use in such a course, or to elicit new research directions.

Author : Zeev Dvir
Publisher : Now Pub
Page : 148 pages
File Size : 46,6 Mb
Release : 2012
Category : Computers
ISBN : 1601986203

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Incidence Theorems and Their Applications by Zeev Dvir Pdf

Describes the way lines, points and other geometric objects intersect each other. Theorems like this have found a large number of applications in the last decades, both in mathematics and in theoretical computer science. This monograph presents some of the seminal results in this area as well as recent developments and applications.

Author : Edward John Specht,Harold Trainer Jones,Keith G. Calkins,Donald H. Rhoads
Publisher : Birkhäuser
Page : 527 pages
File Size : 48,7 Mb
Release : 2015-12-31
Category : Mathematics
ISBN : 9783319237756

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Euclidean Geometry and its Subgeometries by Edward John Specht,Harold Trainer Jones,Keith G. Calkins,Donald H. Rhoads Pdf

In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of these, including all that are needed for this development, are available online at the homepage for the book at www.springer.com. Supplementary material is available online covering construction of complex numbers, arc length, the circular functions, angle measure, and the polygonal form of the Jordan Curve theorem. Euclidean Geometry and Its Subgeometries is intended for advanced students and mature mathematicians, but the proofs are thoroughly worked out to make it accessible to undergraduate students as well. It can be regarded as a completion, updating, and expansion of Hilbert's work, filling a gap in the existing literature.

Author : R. J. Mihalek
Publisher : Academic Press
Page : 233 pages
File Size : 49,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483265209

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Projective Geometry and Algebraic Structures by R. J. Mihalek Pdf

Projective Geometry and Algebraic Structures focuses on the relationship of geometry and algebra, including affine and projective planes, isomorphism, and system of real numbers. The book first elaborates on euclidean, projective, and affine planes, including axioms for a projective plane, algebraic incidence bases, and self-dual axioms. The text then ponders on affine and projective planes, theorems of Desargues and Pappus, and coordination. Topics include algebraic systems and incidence bases, coordinatization theorem, finite projective planes, coordinates, deletion subgeometries, imbedding theorem, and isomorphism. The publication examines projectivities, harmonic quadruples, real projective plane, and projective spaces. Discussions focus on subspaces and dimension, intervals and complements, dual spaces, axioms for a projective space, ordered fields, completeness and the real numbers, real projective plane, and harmonic quadruples. The manuscript is a dependable reference for students and researchers interested in projective planes, system of real numbers, isomorphism, and subspaces and dimensions.

Author : David Hilbert
Publisher : Read Books Ltd
Page : 98 pages
File Size : 44,6 Mb
Release : 2014-07-07
Category : Mathematics
ISBN : 9781473395947

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The Foundations of Geometry by David Hilbert Pdf

This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.