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Author : Lawrence S. Levy
Publisher :
ISBN 13 :
Total Pages : 170 pages
Book Rating : 4.:/5 (114 download)
Download or read book Geometry: Modern Mathematics Via the Euclidean Plane written by Lawrence S. Levy and published by . This book was released on 1970 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lawrence S. Levy
Publisher :
ISBN 13 :
Total Pages : 184 pages
Book Rating : 4.F/5 ( download)
Download or read book Geometry: Modern Mathematics Via the Euclidean Plane written by Lawrence S. Levy and published by . This book was released on 1970 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Edward John Specht
Publisher : Birkhäuser
ISBN 13 : 3319237756
Total Pages : 537 pages
Book Rating : 4.3/5 (192 download)
Download or read book Euclidean Geometry and its Subgeometries written by Edward John Specht and published by Birkhäuser. This book was released on 2015-12-31 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of these, including all that are needed for this development, are available online at the homepage for the book at www.springer.com. Supplementary material is available online covering construction of complex numbers, arc length, the circular functions, angle measure, and the polygonal form of the Jordan Curve theorem. Euclidean Geometry and Its Subgeometries is intended for advanced students and mature mathematicians, but the proofs are thoroughly worked out to make it accessible to undergraduate students as well. It can be regarded as a completion, updating, and expansion of Hilbert's work, filling a gap in the existing literature.
Author : James R. King
Publisher : American Mathematical Soc.
ISBN 13 : 1470463075
Total Pages : 258 pages
Book Rating : 4.4/5 (74 download)
Download or read book Geometry Transformed: Euclidean Plane Geometry Based on Rigid Motions written by James R. King and published by American Mathematical Soc.. This book was released on 2021-04-26 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many paths lead into Euclidean plane geometry. Geometry Transformed offers an expeditious yet rigorous route using axioms based on rigid motions and dilations. Since transformations are available at the outset, interesting theorems can be proved sooner; and proofs can be connected to visual and tactile intuition about symmetry and motion. The reader thus gains valuable experience thinking with transformations, a skill that may be useful in other math courses or applications. For students interested in teaching mathematics at the secondary school level, this approach is particularly useful since geometry in the Common Core State Standards is based on rigid motions. The only prerequisite for this book is a basic understanding of functions. Some previous experience with proofs may be helpful, but students can also learn about proofs by experiencing them in this book—in a context where they can draw and experiment. The eleven chapters are organized in a flexible way to suit a variety of curriculum goals. In addition to a geometrical core that includes finite symmetry groups, there are additional topics on circles and on crystallographic and frieze groups, and a final chapter on affine and Cartesian coordinates. The exercises are a mixture of routine problems, experiments, and proofs.
Author : Euclid
Publisher :
ISBN 13 :
Total Pages : 544 pages
Book Rating : 4.E/5 ( download)
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.
Author : Meighan I. Dillon
Publisher : Springer
ISBN 13 : 3319741357
Total Pages : 356 pages
Book Rating : 4.3/5 (197 download)
Download or read book Geometry Through History written by Meighan I. Dillon and published by Springer. This book was released on 2018-03-21 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the field.
Author : Leonard M. Blumenthal
Publisher : Courier Dover Publications
ISBN 13 : 0486821137
Total Pages : 209 pages
Book Rating : 4.4/5 (868 download)
Download or read book A Modern View of Geometry written by Leonard M. Blumenthal and published by Courier Dover Publications. This book was released on 2017-04-19 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elegant exposition of postulation geometry of planes offers rigorous, lucid treatment of coordination of affine and projective planes, set theory, propositional calculus, affine planes with Desargues and Pappus properties, more. 1961 edition.
Author : Clayton W. Dodge
Publisher : Courier Corporation
ISBN 13 : 9780486434766
Total Pages : 310 pages
Book Rating : 4.4/5 (347 download)
Download or read book Euclidean Geometry and Transformations written by Clayton W. Dodge and published by Courier Corporation. This book was released on 2004-01-01 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
Author : Irving Adler
Publisher : Courier Corporation
ISBN 13 : 0486320499
Total Pages : 420 pages
Book Rating : 4.4/5 (863 download)
Download or read book A New Look at Geometry written by Irving Adler and published by Courier Corporation. This book was released on 2013-10-03 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richly detailed survey of the evolution of geometrical ideas and development of concepts of modern geometry: projective, Euclidean, and non-Euclidean geometry; role of geometry in Newtonian physics, calculus, relativity. Over 100 exercises with answers. 1966 edition.
Author : Jacques Hadamard
Publisher : American Mathematical Soc.
ISBN 13 : 0821843672
Total Pages : 346 pages
Book Rating : 4.8/5 (218 download)
Download or read book Lessons in Geometry written by Jacques Hadamard and published by American Mathematical Soc.. This book was released on 2008 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is a book in the tradition of Euclidean synthetic geometry written by one of the twentieth century's great mathematicians. The original audience was pre-college teachers, but it is useful as well to gifted high school students and college students, in particular, to mathematics majors interested in geometry from a more advanced standpoint. The text starts where Euclid starts, and covers all the basics of plane Euclidean geometry. But this text does much more. It is at once pleasingly classic and surprisingly modern. The problems (more than 450 of them) are well-suited to exploration using the modern tools of dynamic geometry software. For this reason, the present edition includes a CD of dynamic solutions to select problems, created using Texas Instruments' TI-Nspire Learning Software. The TI-Nspire documents demonstrate connections among problems and - through the free trial software included on the CD - will allow the reader to explore and interact with Hadamard's Geometry in new ways. The material also includes introductions to several advanced topics. The exposition is spare, giving only the minimal background needed for a student to explore these topics. Much of the value of the book lies in the problems, whose solutions open worlds to the engaged reader. And so this book is in the Socratic tradition, as well as the Euclidean, in that it demands of the reader both engagement and interaction. A forthcoming companion volume that includes solutions, extensions, and classroom activities related to the problems can only begin to open the treasures offered by this work. We are just fortunate that one of the greatest mathematical minds of recent times has made this effort to show to readers some of the opportunities that the intellectual tradition of Euclidean geometry has to offer."--Jacket.
Author : Owen Byer
Publisher : American Mathematical Soc.
ISBN 13 : 1470457121
Total Pages : 461 pages
Book Rating : 4.4/5 (74 download)
Download or read book Methods for Euclidean Geometry written by Owen Byer and published by American Mathematical Soc.. This book was released on 2010-12-31 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.
Author : John Stillwell
Publisher : Springer Science & Business Media
ISBN 13 : 0387255303
Total Pages : 240 pages
Book Rating : 4.3/5 (872 download)
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
Author : G.E. Martin
Publisher : Springer Science & Business Media
ISBN 13 : 1461257255
Total Pages : 525 pages
Book Rating : 4.4/5 (612 download)
Download or read book The Foundations of Geometry and the Non-Euclidean Plane written by G.E. Martin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Robin Hartshorne
Publisher : Springer Science & Business Media
ISBN 13 : 0387226761
Total Pages : 535 pages
Book Rating : 4.3/5 (872 download)
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.
Author : Matthew Harvey
Publisher : The Mathematical Association of America
ISBN 13 : 1939512115
Total Pages : 561 pages
Book Rating : 4.9/5 (395 download)
Download or read book Geometry Illuminated written by Matthew Harvey and published by The Mathematical Association of America. This book was released on 2015-09-25 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Izu Vaisman
Publisher : CRC Press
ISBN 13 : 1000146340
Total Pages : 290 pages
Book Rating : 4.0/5 (1 download)
Download or read book Foundations of Three-Dimensional Euclidean Geometry written by Izu Vaisman and published by CRC Press. This book was released on 2020-11-26 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Clayton W. Dodge
Publisher : Courier Corporation
ISBN 13 : 0486138429
Total Pages : 306 pages
Book Rating : 4.4/5 (861 download)
Download or read book Euclidean Geometry and Transformations written by Clayton W. Dodge and published by Courier Corporation. This book was released on 2012-04-26 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
