Foundations Of Plane Geometry
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Foundations Of Plane Geometry
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Author : Harvey I. Blau
language : en
Publisher:
Release Date : 2003
Foundations Of Plane Geometry written by Harvey I. Blau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Ideal for users who may have little previous experience with abstraction and proof, this book provides a rigorous and unified--yet straightforward and accessible --exposition of the foundations of Euclidean, hyperbolic, and spherical geometry. Unique in approach, it combines an extended theme--the study of a generalized absolute plane from axioms through classification into the three fundamental classical planes--with a leisurely development that allows ample time for mathematical growth. It is purposefully structured to facilitate the development of analytic and reasoning skills and to promote an awareness of the depth, power, and subtlety of the axiomatic method in general, and of Euclidean and non-Euclidean plane geometry in particular. Focus on one main topic--The axiomatic development of the absolute plane--which is pursued through a classification into Euclidean, hyperbolic, and spherical planes. Presents specific models such as the sphere, the Klein-Betrami hyperbolic model, and the "gap" plane. Gradually presents axioms for absolute plane geometry.
The Foundations Of Geometry And The Non Euclidean Plane
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Author : G.E. Martin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Foundations Of Geometry And The Non Euclidean Plane written by G.E. Martin 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 2012-12-06 with Mathematics categories.
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.
New Foundations For Physical Geometry
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Author : Tim Maudlin
language : en
Publisher:
Release Date : 2014-02
New Foundations For Physical Geometry written by Tim Maudlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02 with Mathematics categories.
Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
The Foundations Of Geometry
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Author : David Hilbert
language : en
Publisher: Read Books Ltd
Release Date : 2015-05-06
The Foundations Of Geometry written by David Hilbert and has been published by Read Books Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-06 with History categories.
This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
Euclidean Plane And Its Relatives
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Author : Anton Petrunin
language : en
Publisher:
Release Date : 2016-09-13
Euclidean Plane And Its Relatives written by Anton Petrunin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-13 with categories.
The book grew from my lecture notes. It is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalistic.
Projective Geometry
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Author : Albrecht Beutelspacher
language : en
Publisher: Cambridge University Press
Release Date : 1998-01-29
Projective Geometry written by Albrecht Beutelspacher and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-29 with Mathematics categories.
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.
Rudiments Of Plane Affine Geometry
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Author : Peter Scherk
language : en
Publisher: Toronto ; Buffalo : University of Toronto Press
Release Date : 1975
Rudiments Of Plane Affine Geometry written by Peter Scherk and has been published by Toronto ; Buffalo : University of Toronto Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
Foundations Of Three Dimensional Euclidean Geometry
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Author : Izu Vaisman
language : en
Publisher: CRC Press
Release Date : 2020-11-26
Foundations Of Three Dimensional Euclidean Geometry written by Izu Vaisman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Mathematics categories.
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.
Euclidean And Non Euclidean Geometry International Student Edition
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Author : Patrick J. Ryan
language : en
Publisher: Cambridge University Press
Release Date : 2009-09-04
Euclidean And Non Euclidean Geometry International Student Edition written by Patrick J. Ryan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-04 with Mathematics categories.
This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic.