Axiomatic Projective Geometry
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Axiomatic Projective Geometry
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Author : A. Heyting
language : en
Publisher: Elsevier
Release Date : 2014-05-12
Axiomatic Projective Geometry written by A. Heyting and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
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.
Axiomatic Projective Geometry
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Author : Arend Heyting
language : en
Publisher:
Release Date : 1963
Axiomatic Projective Geometry written by Arend Heyting and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Mathematics categories.
The Axioms Of Descriptive Geometry
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Author : Alfred North Whitehead
language : en
Publisher:
Release Date : 1960
The Axioms Of Descriptive Geometry written by Alfred North Whitehead and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Geometry categories.
Axiomatic Projective Geometry
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Author : Reuben Louis Goodstein
language : en
Publisher:
Release Date : 1962
Axiomatic Projective Geometry written by Reuben Louis Goodstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Geometry, Projective categories.
Symmetry And Pattern In Projective Geometry
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Author : Eric Lord
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-14
Symmetry And Pattern In Projective Geometry written by Eric Lord and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Mathematics categories.
Symmetry and Pattern in Projective Geometry is a self-contained study of projective geometry which compares and contrasts the analytic and axiomatic methods. The analytic approach is based on homogeneous coordinates, and brief introductions to Plücker coordinates and Grassmann coordinates are presented. This book looks carefully at linear, quadratic, cubic and quartic figures in two, three and higher dimensions. It deals at length with the extensions and consequences of basic theorems such as those of Pappus and Desargues. The emphasis throughout is on special configurations that have particularly interesting symmetry properties. The intricate and novel ideas of ‘Donald’ Coxeter, who is considered one of the great geometers of the twentieth century, are also discussed throughout the text. The book concludes with a useful analysis of finite geometries and a description of some of the remarkable configurations discovered by Coxeter. This book will be appreciated by mathematics students and those wishing to learn more about the subject of geometry. It makes accessible subjects and theorems which are often considered quite complicated and presents them in an easy-to-read and enjoyable manner.
An Axiomatic Approach To Geometry
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Author : Francis Borceux
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-31
An Axiomatic Approach To Geometry written by Francis Borceux and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-31 with Mathematics categories.
Focusing methodologically on those historical aspects that are relevant to supporting intuition in axiomatic approaches to geometry, the book develops systematic and modern approaches to the three core aspects of axiomatic geometry: Euclidean, non-Euclidean and projective. Historically, axiomatic geometry marks the origin of formalized mathematical activity. It is in this discipline that most historically famous problems can be found, the solutions of which have led to various presently very active domains of research, especially in algebra. The recognition of the coherence of two-by-two contradictory axiomatic systems for geometry (like one single parallel, no parallel at all, several parallels) has led to the emergence of mathematical theories based on an arbitrary system of axioms, an essential feature of contemporary mathematics. This is a fascinating book for all those who teach or study axiomatic geometry, and who are interested in the history of geometry or who want to see a complete proof of one of the famous problems encountered, but not solved, during their studies: circle squaring, duplication of the cube, trisection of the angle, construction of regular polygons, construction of models of non-Euclidean geometries, etc. It also provides hundreds of figures that support intuition. Through 35 centuries of the history of geometry, discover the birth and follow the evolution of those innovative ideas that allowed humankind to develop so many aspects of contemporary mathematics. Understand the various levels of rigor which successively established themselves through the centuries. Be amazed, as mathematicians of the 19th century were, when observing that both an axiom and its contradiction can be chosen as a valid basis for developing a mathematical theory. Pass through the door of this incredible world of axiomatic mathematical theories!
Projective Geometry
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Author : H.S.M. Coxeter
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-09
Projective Geometry written by H.S.M. Coxeter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-09 with Mathematics categories.
In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, respectively. The next three chapters develop a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry.
The Axioms Of Projective Geometry
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Author : Alfred North Whitehead
language : en
Publisher:
Release Date : 2015-08-08
The Axioms Of Projective Geometry written by Alfred North Whitehead and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-08 with History categories.
Introduction To Projective Geometry
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Author : C. R. Wylie
language : en
Publisher: Courier Corporation
Release Date : 2011-09-12
Introduction To Projective Geometry written by C. R. Wylie and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-12 with Mathematics categories.
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals.
From Affine To Euclidean Geometry
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Author : W. Szmielew
language : en
Publisher: Springer
Release Date : 1983-08-31
From Affine To Euclidean Geometry written by W. Szmielew and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-08-31 with Mathematics categories.