Plane Euclidean Geometry

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Plane Euclidean Geometry

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Author : Anthony Gardiner
language : en
Publisher: Anchor Books
Release Date : 2012

Plane Euclidean Geometry written by Anthony Gardiner and has been published by Anchor Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Euclid's Elements categories.

Geometry Illuminated

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Author : Matthew Harvey
language : en
Publisher: The Mathematical Association of America
Release Date : 2015-09-25

Geometry Illuminated written by Matthew Harvey and has been published by The Mathematical Association of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-25 with Mathematics categories.

Geometry Illuminated is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very "visual" subject. This book hopes to takes full advantage of that, with an extensive use of illustrations as guides. Geometry Illuminated is divided into four principal parts. Part 1 develops neutral geometry in the style of Hilbert, including a discussion of the construction of measure in that system, ultimately building up to the Saccheri-Legendre Theorem. Part 2 provides a glimpse of classical Euclidean geometry, with an emphasis on concurrence results, such as the nine-point circle. Part 3 studies transformations of the Euclidean plane, beginning with isometries and ending with inversion, with applications and a discussion of area in between. Part 4 is dedicated to the development of the Poincaré disk model, and the study of geometry within that model. While this material is traditional, Geometry Illuminated does bring together topics that are generally not found in a book at this level. Most notably, it explicitly computes parametric equations for the pseudosphere and its geodesics. It focuses less on the nature of axiomatic systems for geometry, but emphasizes rather the logical development of geometry within such a system. It also includes sections dealing with trilinear and barycentric coordinates, theorems that can be proved using inversion, and Euclidean and hyperbolic tilings.

A High School First Course In Euclidean Plane Geometry

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Author : Charles H. Aboughantous
language : en
Publisher: Universal-Publishers
Release Date : 2010-10

A High School First Course In Euclidean Plane Geometry written by Charles H. Aboughantous and has been published by Universal-Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10 with Mathematics categories.

A High School First Course in Euclidean Plane Geometry is intended to be a first course in plane geometry at the high school level. Individuals who do not have a formal background in geometry can also benefit from studying the subject using this book. The content of the book is based on Euclid's five postulates of plane geometry and the most common theorems. It promotes the art and the skills of developing logical proofs. Most of the theorems are provided with detailed proofs. A large number of sample problems are presented throughout the book with detailed solutions. Practice problems are included at the end of each chapter and are presented in three groups: geometric construction problems, computational problems, and theorematical problems. The answers to the computational problems are included at the end of the book. Many of those problems are simplified classic engineering problems that can be solved by average students. The detailed solutions to all the problems in the book are contained in the Solutions Manual. A High School First Course in Euclidean Plane Geometry is the distillation of the author's experience in teaching geometry over many years in U.S. high schools and overseas. The book is best described in the introduction. The prologue offers a study guide to get the most benefits from the book.

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.

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.

Plane And Solid Geometry

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Author : J.M. Aarts
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-28

Plane And Solid Geometry written by J.M. Aarts 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 2009-04-28 with Mathematics categories.

This is a book on Euclidean geometry that covers the standard material in a completely new way, while also introducing a number of new topics that would be suitable as a junior-senior level undergraduate textbook. The author does not begin in the traditional manner with abstract geometric axioms. Instead, he assumes the real numbers, and begins his treatment by introducing such modern concepts as a metric space, vector space notation, and groups, and thus lays a rigorous basis for geometry while at the same time giving the student tools that will be useful in other courses.

Geometry Of Surfaces

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Author : John Stillwell
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-02-03

Geometry Of Surfaces written by John Stillwell 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 1995-02-03 with Mathematics categories.

The geometry of surfaces is an ideal starting point for learning geometry, for, among other reasons, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. This text provides the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. It includes exercises and informal discussions.

Elementary Euclidean Geometry

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Author : C. G. Gibson
language : en
Publisher: Cambridge University Press
Release Date : 2003

Elementary Euclidean Geometry written by C. G. Gibson 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 2003 with Mathematics categories.

This book, first published in 2004, is an example based and self contained introduction to Euclidean geometry with numerous examples and exercises.

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.

An Expedition To Geometry

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Author : S Kumaresan
language : en
Publisher: Springer
Release Date : 2005-04-15

An Expedition To Geometry written by S Kumaresan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-15 with Mathematics categories.

Including Affine and projective classification of Conics, 2 point homogeneity's of the planes, essential isometrics, non euclidean plan geometrics, in this book, the treatment of Geometry goes beyond the Kleinian views.