Axiomatic Geometry
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Axiomatic Geometry
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Author : John M. Lee
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-04-10
Axiomatic Geometry written by John M. Lee and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-10 with Mathematics categories.
The story of geometry is the story of mathematics itself: Euclidean geometry was the first branch of mathematics to be systematically studied and placed on a firm logical foundation, and it is the prototype for the axiomatic method that lies at the foundation of modern mathematics. It has been taught to students for more than two millennia as a mode of logical thought. This book tells the story of how the axiomatic method has progressed from Euclid's time to ours, as a way of understanding what mathematics is, how we read and evaluate mathematical arguments, and why mathematics has achieved the level of certainty it has. It is designed primarily for advanced undergraduates who plan to teach secondary school geometry, but it should also provide something of interest to anyone who wishes to understand geometry and the axiomatic method better. It introduces a modern, rigorous, axiomatic treatment of Euclidean and (to a lesser extent) non-Euclidean geometries, offering students ample opportunities to practice reading and writing proofs while at the same time developing most of the concrete geometric relationships that secondary teachers will need to know in the classroom. -- P. [4] of cover.
Axiomatic Geometry
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Author : Michael C. Gemignani
language : en
Publisher:
Release Date : 1971
Axiomatic Geometry written by Michael C. Gemignani and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
Elementary Differential Geometry
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Author : Christian Bär
language : en
Publisher: Cambridge University Press
Release Date : 2010-05-06
Elementary Differential Geometry written by Christian Bär 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 2010-05-06 with Mathematics categories.
This easy-to-read introduction takes the reader from elementary problems through to current research. Ideal for courses and self-study.
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!
Geometry And Its Applications
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Author : Walter A. Meyer
language : en
Publisher: Elsevier
Release Date : 2006-02-21
Geometry And Its Applications written by Walter A. Meyer and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-21 with Mathematics categories.
Meyer's Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry's usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers. - Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns - Physics - Robotics - Computer vision - Computer graphics - Stability of architectural structures - Molecular biology - Medicine - Pattern recognition - Historical notes included in many chapters
Geometry
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Author : Audun Holme
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Geometry written by Audun Holme 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 2013-03-14 with Mathematics categories.
This book is based on lectures on geometry at the University of Bergen, Norway. Over the years these lectures have covered many different aspects and facets ofthis wonderful field.Consequently it has ofcourse never been possible to give a full and final account ofgeometry as such, at an undergraduate level: A carefully considered selection has always been necessary.The present book constitutes the main central themes of these selections. One of the groups I am aiming at, is future teachers of mathematics. All too often the geometry which goes into the syllabus for teacher-students present the material as pedantic and formalistic, suppressing the very pow erful and dynamic character of this old - and yet so young! - field. A field of mathematical insight, research, history and source of artistic inspiration. And not least important, a foundation for our common cultural heritage. Another motivation is to provide an invitation to mathematics in gen eral. It is an unfortunate fact that today, at a time when mathematics and knowledge of mathematics is more important than ever, phrases like math avoidance and math anxiety are very much in the public vocabulary. An im portant task is seriously attempting to heal these ills. Ills perhaps inflicted on students at an early age, through deficient or even harmful teaching prac tices. Thus the book also aims at an informed public, interested in making a new beginning in math. And in doing so, learning more about this part of our cultural heritage.
Axiomatic Method And Category Theory
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Author : Andrei Rodin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-14
Axiomatic Method And Category Theory written by Andrei Rodin 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 2013-10-14 with Philosophy categories.
This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.
Geometric Crystallography
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Author : P. Engel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Crystallography written by P. Engel 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 Science categories.
In the last decade mathematical crystallography has found increasing interest. Siginificant results have been obtained by algebraic, geometric, and group theoretic methods. Also classical crystallography in three-dimen sional Euclidean space has been extended to higher dimen sions in order to understand better the dimension independent crystallographic properties. The aim of this note is to introduce the reader to the fascinating and rich world of geometric crystallography. The prerequisites for reading it are elementary geometry and topological notations, and basic knowledge of group theory and linear algebra. Crystallography is geometric by its nature. In many cases, geometric arguments are the most appropriate and can thus best be understood. Thus the geometric point of view is emphasized here. The approach is axiomatic start ing from discrete point sets in Euclidean space. Symmetry comes in very soon and plays a central role. Each chapter starts with the necessary definitions and then the subject is treated in two- and three-dimensional space. Subsequent sections give an extension to higher dimensions. Short historical remarks added at the end of the chapters will show the development of the theory. The chapters are main ly self-contained. Frequent cross references, as well as an extended subject index, will help the reader who is only interested in a particular subject.
Exploring Geometry
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Author : Michael Hvidsten
language : en
Publisher: CRC Press
Release Date : 2016-12-08
Exploring Geometry written by Michael Hvidsten and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-08 with Mathematics categories.
Exploring Geometry, Second Edition promotes student engagement with the beautiful ideas of geometry. Every major concept is introduced in its historical context and connects the idea with real-life. A system of experimentation followed by rigorous explanation and proof is central. Exploratory projects play an integral role in this text. Students develop a better sense of how to prove a result and visualize connections between statements, making these connections real. They develop the intuition needed to conjecture a theorem and devise a proof of what they have observed. Features: Second edition of a successful textbook for the first undergraduate course Every major concept is introduced in its historical context and connects the idea with real life Focuses on experimentation Projects help enhance student learning All major software programs can be used; free software from author