Download or read book Foundations of Incidence Geometry written by Johannes Ueberberg and published by Springer Science & Business Media. This book was released on 2011-08-26 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Incidence Geometry written by Bart De Bruyn and published by Birkhäuser. This book was released on 2016-11-09 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Handbook of Incidence Geometry written by Francis Buekenhout and published by North-Holland. This book was released on 1995 with total page 1440 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Geometry of Incidence written by Harold Laird Dorwart and published by . This book was released on 1966 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Projective Geometry and Algebraic Structures written by R. J. Mihalek and published by Academic Press. This book was released on 2014-05-10 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Geometry of Incidence written by Harold L. Dorwart and published by . This book was released on 1974 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Projective Geometry written by Albrecht Beutelspacher and published by Cambridge University Press. This book was released on 1998-01-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Polynomial Methods and Incidence Theory written by Adam Sheffer and published by Cambridge University Press. This book was released on 2022-03-24 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough yet accessible introduction to the mathematical breakthroughs achieved by using new polynomial methods in the past decade.
Download or read book Axiomatic Projective Geometry written by A. Heyting and published by Elsevier. This book was released on 2014-05-12 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Perspectives on Projective Geometry written by Jürgen Richter-Gebert and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Incidence Axioms for Affine Geometry written by Marshall Hall (Jr) and published by . This book was released on 1971 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book The Contest Problem Book VI written by Leo J. Schneider and published by Mathematical Assn of Amer. This book was released on 2000 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Geometry of Incidence written by Harold Laird Dorwart and published by . This book was released on 1966 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Foundations of Geometry written by David Hilbert and published by . This book was released on 1902 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Geometry written by Gerard Venema and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Normal 0 false false false Foundations of Geometry, Second Edition is written to help enrich the education of all mathematics majors and facilitate a smooth transition into more advanced mathematics courses. The text also implements the latest national standards and recommendations regarding geometry for the preparation of high school mathematics teachers--and encourages students to make connections between their college courses and classes they will later teach. This text's coverage begins with Euclid's Elements, lays out a system of axioms for geometry, and then moves on to neutral geometry, Euclidian and hyperbolic geometries from an axiomatic point of view, and then non-Euclidean geometry. Good proof-writing skills are emphasized, along with a historical development of geometry. The Second Edition streamlines and reorganizes material in order to reach coverage of neutral geometry as early as possible, adds more exercises throughout, and facilitates use of the open-source software Geogebra. This text is ideal for an undergraduate course in axiomatic geometry for future high school geometry teachers, or for any student who has not yet encountered upper-level math, such as real analysis or abstract algebra. It assumes calculus and linear algebra as prerequisites.
Download or read book Incidence Theorems and Their Applications written by Zeev Dvir and published by Now Pub. This book was released on 2012 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Points and Lines written by Ernest E. Shult and published by Springer Science & Business Media. This book was released on 2010-12-13 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
