the real projective plane

Download Book The Real Projective Plane in PDF format. You can Read Online The Real Projective Plane here in PDF, EPUB, Mobi or Docx formats.

The Real Projective Plane

Author : H.S.M. Coxeter
ISBN : 9781461227342
Genre : Mathematics
File Size : 59. 59 MB
Format : PDF, ePub, Mobi
Download : 802
Read : 406

Get This Book


Along with many small improvements, this revised edition contains van Yzeren's new proof of Pascal's theorem (§1.7) and, in Chapter 2, an improved treatment of order and sense. The Sylvester-Gallai theorem, instead of being introduced as a curiosity, is now used as an essential step in the theory of harmonic separation (§3.34). This makes the logi cal development self-contained: the footnotes involving the References (pp. 214-216) are for comparison with earlier treatments, and to give credit where it is due, not to fill gaps in the argument. H.S.M.C. November 1992 v Preface to the Second Edition Why should one study the real plane? To this question, put by those who advocate the complex plane, or geometry over a general field, I would reply that the real plane is an easy first step. Most of the prop erties are closely analogous, and the real field has the advantage of intuitive accessibility. Moreover, real geometry is exactly what is needed for the projective approach to non· Euclidean geometry. Instead of introducing the affine and Euclidean metrics as in Chapters 8 and 9, we could just as well take the locus of 'points at infinity' to be a conic, or replace the absolute involution by an absolute polarity.

Models Of The Real Projective Plane

Author : Francois Apery
ISBN : 9783322895691
Genre : Technology & Engineering
File Size : 20. 15 MB
Format : PDF, ePub, Mobi
Download : 119
Read : 726

Get This Book


In the present time, objects generated by computers are replacing models made from wood, wire, and plaster. It is interesting to see how computer graphics can help us to understand the geometry of surfaces and illustrate some recent results on representations of the real projective plane.

Projective Geometry And Algebraic Structures

Author : R. J. Mihalek
ISBN : 9781483265209
Genre : Mathematics
File Size : 61. 27 MB
Format : PDF, ePub, Mobi
Download : 883
Read : 463

Get This Book


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.

Pencils Of Cubics And Algebraic Curves In The Real Projective Plane

Author : Sverine Fiedler Le Touz
ISBN : 1138590517
Genre :
File Size : 70. 61 MB
Format : PDF, Docs
Download : 870
Read : 1006

Get This Book


Pencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP2. Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. The first part of the book answers questions related to using rational cubics and pencils of cubics. The other two parts deal with configurations of eight points in convex position, and applications and results around Hilbert's sixteenth problem.

Perspectives On Projective Geometry

Author : Jürgen Richter-Gebert
ISBN : 3642172865
Genre : Mathematics
File Size : 20. 14 MB
Format : PDF, ePub
Download : 928
Read : 1260

Get This Book


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.

Oriented Projective Geometry

Author : Jorge Stolfi
ISBN : 9781483265193
Genre : Mathematics
File Size : 22. 7 MB
Format : PDF, Kindle
Download : 249
Read : 373

Get This Book


Oriented Projective Geometry: A Framework for Geometric Computations proposes that oriented projective geometry is a better framework for geometric computations than classical projective geometry. The aim of the book is to stress the value of oriented projective geometry for practical computing and develop it as a rich, consistent, and effective tool for computer programmers. The monograph is comprised of 20 chapters. Chapter 1 gives a quick overview of classical and oriented projective geometry on the plane, and discusses their advantages and disadvantages as computational models. Chapters 2 through 7 define the canonical oriented projective spaces of arbitrary dimension, the operations of join and meet, and the concept of relative orientation. Chapter 8 defines projective maps, the space transformations that preserve incidence and orientation; these maps are used in chapter 9 to define abstract oriented projective spaces. Chapter 10 introduces the notion of projective duality. Chapters 11, 12, and 13 deal with projective functions, projective frames, relative coordinates, and cross-ratio. Chapter 14 tells about convexity in oriented projective spaces. Chapters 15, 16, and 17 show how the affine, Euclidean, and linear vector spaces can be emulated with the oriented projective space. Finally, chapters 18 through 20 discuss the computer representation and manipulation of lines, planes, and other subspaces. Computer scientists and programmers will find this text invaluable.

Linear Algebra And Projective Geometry

Author : Reinhold Baer
ISBN : 9780486154664
Genre : Mathematics
File Size : 39. 62 MB
Format : PDF
Download : 201
Read : 413

Get This Book


Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.

Mathematical Models

Author : Gerd Fischer
ISBN : 9783658188658
Genre : Mathematics
File Size : 44. 28 MB
Format : PDF, Mobi
Download : 155
Read : 493

Get This Book


This book presents beautiful photos of mathematical models of geometric surfaces made from a variety of materials including plaster, metal, paper, wood, and string. The construction of these models at the time (of Felix Klein and others) was not an end in itself, but was accompanied by mathematical research especially in the field of algebraic geometry. The models were used to illustrate the mathematical objects defined by abstract formulas, either as equations or parameterizations. In the second part of the book, the models are explained by experts in the field of geometry. This book is a reprint thirty years after the original publication in 1986 with a new preface by Gert-Martin Greuel. The models have a timeless appeal and a historical value.

An Outline Of Projective Geometry

Author : Lynn E. Garner
ISBN : UOM:39015015621587
Genre : Mathematics
File Size : 35. 78 MB
Format : PDF, ePub
Download : 749
Read : 576

Get This Book



An Introduction To Finite Projective Planes

Author : Abraham Adrian Albert
ISBN : 9780486789941
Genre : Mathematics
File Size : 34. 91 MB
Format : PDF, ePub
Download : 449
Read : 572

Get This Book


Text for both beginning and advanced undergraduate and graduate students covers finite planes, field planes, coordinates in an arbitrary plane, central collineations and the little Desargues' property, the fundamental theorem, and non-Desarguesian planes. 1968 edition.

Top Download:

Best Books