Foundations Of Incidence Geometry

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Foundations of Incidence Geometry

Author : Johannes Ueberberg
Publisher : Springer Science & Business Media
ISBN 13 : 3642209726
Total Pages : 259 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Foundations of Incidence Geometry by : Johannes Ueberberg

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.

Handbook of Incidence Geometry

Author : Francis Buekenhout
Publisher : North-Holland
ISBN 13 :
Total Pages : 1440 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Handbook of Incidence Geometry by : Francis Buekenhout

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.

Foundations of Geometry

Author : Karol Borsuk
Publisher : Courier Dover Publications
ISBN 13 : 0486828093
Total Pages : 465 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Foundations of Geometry by : Karol Borsuk

Download or read book Foundations of Geometry written by Karol Borsuk and published by Courier Dover Publications. This book was released on 2018-11-14 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Albrecht Beutelspacher
Publisher : Cambridge University Press
ISBN 13 : 9780521483643
Total Pages : 272 pages
Book Rating : 4.4/5 (836 download)

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Book Synopsis Projective Geometry by : Albrecht Beutelspacher

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.

An Introduction to Incidence Geometry

Author : Bart De Bruyn
Publisher : Birkhäuser
ISBN 13 : 3319438115
Total Pages : 380 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis An Introduction to Incidence Geometry by : Bart De Bruyn

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.

Foundations of Three-Dimensional Euclidean Geometry

Author : Izu Vaisman
Publisher : CRC Press
ISBN 13 : 1000110494
Total Pages : 287 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Foundations of Three-Dimensional Euclidean Geometry by : Izu Vaisman

Download or read book Foundations of Three-Dimensional Euclidean Geometry written by Izu Vaisman and published by CRC Press. This book was released on 2020-11-25 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Foundations of Geometry

Author : Gerard Venema
Publisher :
ISBN 13 : 9780136020585
Total Pages : 0 pages
Book Rating : 4.0/5 (25 download)

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Book Synopsis Foundations of Geometry by : Gerard Venema

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.

The Foundations of Geometry

Author : David Hilbert
Publisher :
ISBN 13 :
Total Pages : 158 pages
Book Rating : 4.3/5 (129 download)

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Book Synopsis The Foundations of Geometry by : David Hilbert

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:

The Foundations of Geometry and the Non-Euclidean Plane

Author : G.E. Martin
Publisher : Springer Science & Business Media
ISBN 13 : 1461257255
Total Pages : 525 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Foundations of Geometry and the Non-Euclidean Plane by : G.E. Martin

Download or read book The Foundations of Geometry and the Non-Euclidean Plane written by G.E. Martin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The remaining chap ters may then be used for either a regular course or independent study courses. Another possibility, which is also especially suited for in-service teachers of high school geometry, is to survey the the fundamentals of absolute geometry (Chapters 1 -20) very quickly and begin earnest study with the theory of parallels and isometries (Chapters 21 -30). The text is self-contained, except that the elementary calculus is assumed for some parts of the material on advanced hyperbolic geometry (Chapters 31 -34). There are over 650 exercises, 30 of which are 10-part true-or-false questions. A rigorous ruler-and-protractor axiomatic development of the Euclidean and hyperbolic planes, including the classification of the isometries of these planes, is balanced by the discussion about this development. Models, such as Taxicab Geometry, are used exten sively to illustrate theory. Historical aspects and alternatives to the selected axioms are prominent. The classical axiom systems of Euclid and Hilbert are discussed, as are axiom systems for three and four-dimensional absolute geometry and Pieri's system based on rigid motions. The text is divided into three parts. The Introduction (Chapters 1 -4) is to be read as quickly as possible and then used for ref erence if necessary.

Ordered Incidence Geometry and the Geometric Foundations of Convexity Theory

Author : Adi Ben-Israel
Publisher :
ISBN 13 :
Total Pages : 57 pages
Book Rating : 4.:/5 (115 download)

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Book Synopsis Ordered Incidence Geometry and the Geometric Foundations of Convexity Theory by : Adi Ben-Israel

Download or read book Ordered Incidence Geometry and the Geometric Foundations of Convexity Theory written by Adi Ben-Israel and published by . This book was released on 1984 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Ordered Incidence Geometry, that is a geometry with certain axioms of incidence and order is proposed as a minimal setting for the fundamental convexity theorems, such as the hyperplane separation theorem and the theorems of Radon and Helly. These theorems are usually stated, proved, understood and/or applied in the context of a linear vector space, but they require only incidence and order, (and for separation, completeness), and none of the linear structure of a vector space.

Perspectives on Projective Geometry

Author : Jürgen Richter-Gebert
Publisher : Springer Science & Business Media
ISBN 13 : 3642172865
Total Pages : 573 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Perspectives on Projective Geometry by : Jürgen Richter-Gebert

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.

Roads to Geometry

Author : Edward C. Wallace
Publisher : Waveland Press
ISBN 13 : 1478632046
Total Pages : 510 pages
Book Rating : 4.4/5 (786 download)

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Book Synopsis Roads to Geometry by : Edward C. Wallace

Download or read book Roads to Geometry written by Edward C. Wallace and published by Waveland Press. This book was released on 2015-10-23 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now available from Waveland Press, the Third Edition of Roads to Geometry is appropriate for several kinds of students. Pre-service teachers of geometry are provided with a thorough yet accessible treatment of plane geometry in a historical context. Mathematics majors will find its axiomatic development sufficiently rigorous to provide a foundation for further study in the areas of Euclidean and non-Euclidean geometry. By using the SMSG postulate set as a basis for the development of plane geometry, the authors avoid the pitfalls of many “foundations of geometry” texts that encumber the reader with such a detailed development of preliminary results that many other substantive and elegant results are inaccessible in a one-semester course. At the end of each section is an ample collection of exercises of varying difficulty that provides problems that both extend and clarify results of that section, as well as problems that apply those results. At the end of chapters 3–7, a summary list of the new definitions and theorems of each chapter is included.

Points and Lines

Author : Ernest E. Shult
Publisher : Springer Science & Business Media
ISBN 13 : 3642156274
Total Pages : 682 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Points and Lines by : Ernest E. Shult

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.

The Foundations of Geometry

Author : Gerard Venema
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 456 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Foundations of Geometry by : Gerard Venema

Download or read book The Foundations of Geometry written by Gerard Venema and published by Prentice Hall. This book was released on 2006 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: For sophomore/junior-level courses in Geometry; especially appropriate for students that will go on to teach high-school mathematics. This text comfortably serves as a bridge between lower-level mathematics courses (calculus and linear algebra) and upper-level courses (real analysis and abstract algebra). It fully implements the latest national standards and recommendations regarding geometry for the preparation of high school mathematics teachers. Foundations of Geometry particularly teaches good proof-writing skills, emphasizes the historical development of geometry, and addresses certain issues concerning the place of geometry in human culture.

Foundations of Geometry

Author : Karol Borsuk
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (231 download)

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Book Synopsis Foundations of Geometry by : Karol Borsuk

Download or read book Foundations of Geometry written by Karol Borsuk and published by . This book was released on 1960 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Compact Projective Planes

Author : Helmut Salzmann
Publisher : Walter de Gruyter
ISBN 13 : 3110876833
Total Pages : 705 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Compact Projective Planes by : Helmut Salzmann

Download or read book Compact Projective Planes written by Helmut Salzmann and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Geometry

Author : Richard S. Millman
Publisher : Springer Science & Business Media
ISBN 13 : 9780387974125
Total Pages : 394 pages
Book Rating : 4.9/5 (741 download)

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Book Synopsis Geometry by : Richard S. Millman

Download or read book Geometry written by Richard S. Millman and published by Springer Science & Business Media. This book was released on 1993-05-07 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry: A Metric Approach with Models, imparts a real feeling for Euclidean and non-Euclidean (in particular, hyperbolic) geometry. Intended as a rigorous first course, the book introduces and develops the various axioms slowly, and then, in a departure from other texts, continually illustrates the major definitions and axioms with two or three models, enabling the reader to picture the idea more clearly. The second edition has been expanded to include a selection of expository exercises. Additionally, the authors have designed software with computational problems to accompany the text. This software may be obtained from George Parker.