Author: Johannes Ueberberg
Publisher: Springer Science & Business Media
ISBN: 3642209726
Category : Mathematics
Languages : en
Pages : 259
Book Description
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.
Foundations of Incidence Geometry
Author: Johannes Ueberberg
Publisher: Springer Science & Business Media
ISBN: 3642209726
Category : Mathematics
Languages : en
Pages : 259
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 3642209726
Category : Mathematics
Languages : en
Pages : 259
Book Description
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.
An Introduction to Incidence Geometry
Author: Bart De Bruyn
Publisher: Birkhäuser
ISBN: 3319438115
Category : Mathematics
Languages : en
Pages : 380
Book Description
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.
Publisher: Birkhäuser
ISBN: 3319438115
Category : Mathematics
Languages : en
Pages : 380
Book Description
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
Author: Francis Buekenhout
Publisher: North-Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 1440
Book Description
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.
Publisher: North-Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 1440
Book Description
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.
The Geometry of Incidence
Author: Harold Laird Dorwart
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 184
Book Description
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 184
Book Description
The Geometry of Incidence
Author: Harold L. Dorwart
Publisher:
ISBN:
Category :
Languages : en
Pages : 159
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 159
Book Description
Projective Geometry
Author: Albrecht Beutelspacher
Publisher: Cambridge University Press
ISBN: 9780521483643
Category : Mathematics
Languages : en
Pages : 272
Book Description
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.
Publisher: Cambridge University Press
ISBN: 9780521483643
Category : Mathematics
Languages : en
Pages : 272
Book Description
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.
Polynomial Methods and Incidence Theory
Author: Adam Sheffer
Publisher: Cambridge University Press
ISBN: 1108832490
Category : Mathematics
Languages : en
Pages : 263
Book Description
A thorough yet accessible introduction to the mathematical breakthroughs achieved by using new polynomial methods in the past decade.
Publisher: Cambridge University Press
ISBN: 1108832490
Category : Mathematics
Languages : en
Pages : 263
Book Description
A thorough yet accessible introduction to the mathematical breakthroughs achieved by using new polynomial methods in the past decade.
Axiomatic Projective Geometry
Author: A. Heyting
Publisher: Elsevier
ISBN: 1483259315
Category : Mathematics
Languages : en
Pages : 161
Book Description
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.
Publisher: Elsevier
ISBN: 1483259315
Category : Mathematics
Languages : en
Pages : 161
Book Description
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.
Incidence Axioms for Affine Geometry
Author: Marshall Hall (Jr)
Publisher:
ISBN:
Category :
Languages : en
Pages : 23
Book Description
In terms of incidence alone it is possible to define an affine plane, as Artin does, by calling lines parallel if they do not intersect, and basing the definition on the Euclidean axiom that there is a unique parallel to a line through a point not on the line. In higher dimensions one can define affine geometry by deleting the points and lines of a hyperplane from a projective geometry, using the axioms of Veblen and Young. It is an easy exercise to show that the Artin approach and that of Veblen and Young agree in the definition of an affine plane. But in higher dimensions it is not clear how an affine geometry can be defined directly so that it can be shown to arise from a projective geometry by deleting the points and lines of a hyperplane. This paper gives a set of axioms which have this property. (Author).
Publisher:
ISBN:
Category :
Languages : en
Pages : 23
Book Description
In terms of incidence alone it is possible to define an affine plane, as Artin does, by calling lines parallel if they do not intersect, and basing the definition on the Euclidean axiom that there is a unique parallel to a line through a point not on the line. In higher dimensions one can define affine geometry by deleting the points and lines of a hyperplane from a projective geometry, using the axioms of Veblen and Young. It is an easy exercise to show that the Artin approach and that of Veblen and Young agree in the definition of an affine plane. But in higher dimensions it is not clear how an affine geometry can be defined directly so that it can be shown to arise from a projective geometry by deleting the points and lines of a hyperplane. This paper gives a set of axioms which have this property. (Author).
The Contest Problem Book VI
Author: Leo J. Schneider
Publisher: Mathematical Assn of Amer
ISBN: 9780883856420
Category : Mathematics
Languages : en
Pages : 212
Book Description
The focus in this book is on projective geometry and its roots in 'classical geometry', a pursuit which the authors feel has been largely neglected in the abstract-oriented mathematics of the twentieth century. Dorwart and Berger quickly lead into a discussion of the geometry of incidence, tracing its formulation from Euclid through David Hilbert. The reader is expected to do much of the mathematics within, and the book will be suitable for anybody familiar with only a little geometry.
Publisher: Mathematical Assn of Amer
ISBN: 9780883856420
Category : Mathematics
Languages : en
Pages : 212
Book Description
The focus in this book is on projective geometry and its roots in 'classical geometry', a pursuit which the authors feel has been largely neglected in the abstract-oriented mathematics of the twentieth century. Dorwart and Berger quickly lead into a discussion of the geometry of incidence, tracing its formulation from Euclid through David Hilbert. The reader is expected to do much of the mathematics within, and the book will be suitable for anybody familiar with only a little geometry.