Axiomatic Geometry

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Axiomatic Geometry

Author : John M. Lee
Publisher : American Mathematical Soc.
ISBN 13 : 0821884786
Total Pages : 490 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Axiomatic Geometry by : John M. Lee

Download or read book Axiomatic Geometry written by John M. Lee and published by American Mathematical Soc.. This book was released on 2013-04-10 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Axiomatic Approach to Geometry

Author : Francis Borceux
Publisher : Springer Science & Business Media
ISBN 13 : 3319017306
Total Pages : 410 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis An Axiomatic Approach to Geometry by : Francis Borceux

Download or read book An Axiomatic Approach to Geometry written by Francis Borceux and published by Springer Science & Business Media. This book was released on 2013-10-31 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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!

Axiomatic Geometry

Author : Michael C. Gemignani
Publisher :
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Axiomatic Geometry by : Michael C. Gemignani

Download or read book Axiomatic Geometry written by Michael C. Gemignani and published by . This book was released on 1971 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Euclidean Geometry

Author : David M. Clark
Publisher : American Mathematical Soc.
ISBN 13 : 0821889850
Total Pages : 157 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Euclidean Geometry by : David M. Clark

Download or read book Euclidean Geometry written by David M. Clark and published by American Mathematical Soc.. This book was released on 2012-06-26 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry has been an essential element in the study of mathematics since antiquity. Traditionally, we have also learned formal reasoning by studying Euclidean geometry. In this book, David Clark develops a modern axiomatic approach to this ancient subject, both in content and presentation. Mathematically, Clark has chosen a new set of axioms that draw on a modern understanding of set theory and logic, the real number continuum and measure theory, none of which were available in Euclid's time. The result is a development of the standard content of Euclidean geometry with the mathematical precision of Hilbert's foundations of geometry. In particular, the book covers all the topics listed in the Common Core State Standards for high school synthetic geometry. The presentation uses a guided inquiry, active learning pedagogy. Students benefit from the axiomatic development because they themselves solve the problems and prove the theorems with the instructor serving as a guide and mentor. Students are thereby empowered with the knowledge that they can solve problems on their own without reference to authority. This book, written for an undergraduate axiomatic geometry course, is particularly well suited for future secondary school teachers. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Axiomatic Projective Geometry

Author : A. Heyting
Publisher : Elsevier
ISBN 13 : 1483259315
Total Pages : 161 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Axiomatic Projective Geometry by : A. Heyting

Download or read book Axiomatic Projective Geometry written by A. Heyting and published by Elsevier. This book was released on 2014-05-12 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometry of Vector Sheaves

Author : Anastasios Mallios
Publisher : Springer Science & Business Media
ISBN 13 : 9401150060
Total Pages : 457 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Geometry of Vector Sheaves by : Anastasios Mallios

Download or read book Geometry of Vector Sheaves written by Anastasios Mallios and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (CINFINITY) manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasised. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology (`differential spaces'), to non-linear PDEs (generalised functions). Thus, more general applications, which are no longer `smooth' in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the `world around us is far from being smooth enough'. Audience: This work is intended for postgraduate students and researchers whose work involves differential geometry, global analysis, analysis on manifolds, algebraic topology, sheaf theory, cohomology, functional analysis or abstract harmonic analysis.

Geometry: Euclid and Beyond

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
ISBN 13 : 0387226761
Total Pages : 535 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Geometry: Euclid and Beyond by : Robin Hartshorne

Download or read book Geometry: Euclid and Beyond written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.

Geometric Trilogy

Author : Francis Borceux
Publisher : Springer
ISBN 13 : 9783319018041
Total Pages : 1350 pages
Book Rating : 4.0/5 (18 download)

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Book Synopsis Geometric Trilogy by : Francis Borceux

Download or read book Geometric Trilogy written by Francis Borceux and published by Springer. This book was released on 2013-11-09 with total page 1350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Trilogy intends to introduce the reader to the multiple complementary aspects of geometry, paying attention to the historical birth and growth of the ideas and results, and concluding with a contemporary presentation of the various topics considered. Three essentially independent volumes approach geometry via the axiomatic, the algebraic and the differential points of view. The “ruler and compass” approach to geometry, developed by the Greek mathematicians of the Antiquity, remained the only reference in Geometry – and even in Mathematics -- for more than two millenniums. The fruitless efforts for solving the so-called “classical problems” of Greek geometry lead eventually to a deeper reflection on the axiomatic bases of geometry, and in particular to the discovery of projective geometry and non-Euclidean geometries. During the Renaissance, mathematicians start liberating themselves from the “ruler and compass” dogma and use algebraic techniques to investigate geometric situations. The nineteenth century, with the birth of linear algebra and the theory of polynomials, opens new doors and in particular, the fascinating world of algebraic curves. The introduction of differential calculus during the eighteenth century allows widening considerably the range of curves and surfaces considered. The notion of curvature –under multiple forms -- imposes itself as an essential tool for studying the properties of curves and surfaces. And a keen study of some geometrical properties of surfaces gives rise to the theory of algebraic topology. This trilogy is of interest to all those who have to teach or study geometry and need to have a good global overview of the numerous facets of this fascinating topic. It provides both the intuitive and the technical ingredients needed to find one’s way through Euclidean, non-Euclidean, projective, algebraic or differential geometry at a high level.

A Vector Space Approach to Geometry

Author : Melvin Hausner
Publisher : Courier Dover Publications
ISBN 13 : 0486835391
Total Pages : 417 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis A Vector Space Approach to Geometry by : Melvin Hausner

Download or read book A Vector Space Approach to Geometry written by Melvin Hausner and published by Courier Dover Publications. This book was released on 2018-10-17 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fascinating exploration of the correlation between geometry and linear algebra, this text also offers elementary explanations of the role of geometry in other branches of math and science. 1965 edition.

Roads to Geometry

Author : Edward C. Wallace
Publisher : Waveland Press
ISBN 13 : 1478632046
Total Pages : 510 pages
Book Rating : 4.4/5 (786 download)

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Book Synopsis Roads to Geometry by : Edward C. Wallace

Download or read book Roads to Geometry written by Edward C. Wallace and published by Waveland Press. This book was released on 2015-10-23 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now available from Waveland Press, the Third Edition of Roads to Geometry is appropriate for several kinds of students. Pre-service teachers of geometry are provided with a thorough yet accessible treatment of plane geometry in a historical context. Mathematics majors will find its axiomatic development sufficiently rigorous to provide a foundation for further study in the areas of Euclidean and non-Euclidean geometry. By using the SMSG postulate set as a basis for the development of plane geometry, the authors avoid the pitfalls of many “foundations of geometry” texts that encumber the reader with such a detailed development of preliminary results that many other substantive and elegant results are inaccessible in a one-semester course. At the end of each section is an ample collection of exercises of varying difficulty that provides problems that both extend and clarify results of that section, as well as problems that apply those results. At the end of chapters 3–7, a summary list of the new definitions and theorems of each chapter is included.

The Foundations of Geometry

Author : David Hilbert
Publisher : Read Books Ltd
ISBN 13 : 1473395941
Total Pages : 139 pages
Book Rating : 4.4/5 (733 download)

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Book Synopsis The Foundations of Geometry by : David Hilbert

Download or read book The Foundations of Geometry written by David Hilbert and published by Read Books Ltd. This book was released on 2015-05-06 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Euclid's Elements

Author : Euclid
Publisher :
ISBN 13 :
Total Pages : 544 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Euclid's Elements by : Euclid

Download or read book Euclid's Elements written by Euclid and published by . This book was released on 2002 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary" --from book jacket.

The Four Pillars of Geometry

Author : John Stillwell
Publisher : Springer Science & Business Media
ISBN 13 : 0387255303
Total Pages : 240 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis The Four Pillars of Geometry by : John Stillwell

Download or read book The Four Pillars of Geometry written by John Stillwell and published by Springer Science & Business Media. This book was released on 2005-08-09 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises

Introduction to Projective Geometry

Author : C. R. Wylie
Publisher : Courier Corporation
ISBN 13 : 0486141705
Total Pages : 578 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Introduction to Projective Geometry by : C. R. Wylie

Download or read book Introduction to Projective Geometry written by C. R. Wylie and published by Courier Corporation. This book was released on 2011-09-12 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Kiselev's Geometry

Author : Andreĭ Petrovich Kiselev
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Kiselev's Geometry by : Andreĭ Petrovich Kiselev

Download or read book Kiselev's Geometry written by Andreĭ Petrovich Kiselev and published by . This book was released on 2008 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume completes the English adaptation of a classical Russian textbook in elementary Euclidean geometry. The 1st volume subtitled "Book I. Planimetry" was published in 2006 (ISBN 0977985202). This 2nd volume (Book II. Stereometry) covers solid geometry, and contains a chapter on vectors, foundations, and introduction in non-Euclidean geometry added by the translator. The book intended for high-school and college students, and their teachers. Includes 317 exercises, index, and bibliography.

Foundations of Geometry

Author : Gerard Venema
Publisher :
ISBN 13 : 9780136020585
Total Pages : 0 pages
Book Rating : 4.0/5 (25 download)

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Book Synopsis Foundations of Geometry by : Gerard Venema

Download or read book Foundations of Geometry written by Gerard Venema and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Normal 0 false false false Foundations of Geometry, Second Edition is written to help enrich the education of all mathematics majors and facilitate a smooth transition into more advanced mathematics courses. The text also implements the latest national standards and recommendations regarding geometry for the preparation of high school mathematics teachers--and encourages students to make connections between their college courses and classes they will later teach. This text's coverage begins with Euclid's Elements, lays out a system of axioms for geometry, and then moves on to neutral geometry, Euclidian and hyperbolic geometries from an axiomatic point of view, and then non-Euclidean geometry. Good proof-writing skills are emphasized, along with a historical development of geometry. The Second Edition streamlines and reorganizes material in order to reach coverage of neutral geometry as early as possible, adds more exercises throughout, and facilitates use of the open-source software Geogebra. This text is ideal for an undergraduate course in axiomatic geometry for future high school geometry teachers, or for any student who has not yet encountered upper-level math, such as real analysis or abstract algebra. It assumes calculus and linear algebra as prerequisites.

Geometry and Its Applications

Author : Walter A. Meyer
Publisher : Elsevier
ISBN 13 : 0080478034
Total Pages : 560 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Geometry and Its Applications by : Walter A. Meyer

Download or read book Geometry and Its Applications written by Walter A. Meyer and published by Elsevier. This book was released on 2006-02-21 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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