Taxicab Geometry

An Adventure in Non-Euclidean Geometry

Author: Eugene F. Krause

Publisher: Courier Corporation

ISBN: 048613606X

Category: Mathematics

Page: 96

View: 4706

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Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Illustrated topics include applications to urban geography and comparisons to Euclidean geometry. Selected answers to problems.

Taxicab Geometry

An Adventure in Non-Euclidean Geometry

Author: Eugene F. Krause

Publisher: Courier Corporation

ISBN: 0486252027

Category: Mathematics

Page: 88

View: 998

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Develops a simple non-Euclidean geometry and explores some of its practical applications through graphs, research problems, and exercises. Includes selected answers.

The Last Recreations

Hydras, Eggs, and Other Mathematical Mystifications

Author: Martin Gardner

Publisher: Springer Science & Business Media

ISBN: 0387258272

Category: Mathematics

Page: 392

View: 4982

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Of all of Martin Gardners writings, none gained him a wider audience or was more central to his reputation than his Mathematical Recreations column in Scientific American - which virtually defined the genre of popular mathematics writing for a generation. Flatland, Hydras and Eggs: Mathematical Mystifications is the final collection of these columns, covering the period roughly from 1979 to Gardners retirement in 1986. As always in his published collections, Gardner includes letters commenting on the ideas presented in his articles. These columns show him at the top of his form and should not be missed by anyone with an interest in mathematics.

The Foundations of Geometry and the Non-Euclidean Plane

Author: G.E. Martin

Publisher: Springer Science & Business Media

ISBN: 1461257255

Category: Mathematics

Page: 512

View: 4657

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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.

College Geometry: Using the Geometer's Sketchpad, 1st Edition

Using the Geometer's Sketchpad

Author: Barbara E. Reynolds,William E. Fenton

Publisher: Wiley Global Education

ISBN: 1118213408

Category: Mathematics

Page: 380

View: 6332

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From two authors who embrace technology in the classroom and value the role of collaborative learning comes College Geometry Using The Geometer's Sketchpad, a book that is ideal for geometry courses for both mathematics and math education majors. The book's truly discovery-based approach guides students to learn geometry through explorations of topics ranging from triangles and circles to transformational, taxicab, and hyperbolic geometries. In the process, students hone their understanding of geometry and their ability to write rigorous mathematical proofs.

Geometry, Relativity and the Fourth Dimension

Author: Rudolf Rucker

Publisher: Courier Corporation

ISBN: 0486140334

Category: Science

Page: 160

View: 3436

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Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.

How Round Is Your Circle?

Where Engineering and Mathematics Meet

Author: John Bryant,Chris Sangwin

Publisher: Princeton University Press

ISBN: 1400837952

Category: Mathematics

Page: 320

View: 7071

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How do you draw a straight line? How do you determine if a circle is really round? These may sound like simple or even trivial mathematical problems, but to an engineer the answers can mean the difference between success and failure. How Round Is Your Circle? invites readers to explore many of the same fundamental questions that working engineers deal with every day--it's challenging, hands-on, and fun. John Bryant and Chris Sangwin illustrate how physical models are created from abstract mathematical ones. Using elementary geometry and trigonometry, they guide readers through paper-and-pencil reconstructions of mathematical problems and show them how to construct actual physical models themselves--directions included. It's an effective and entertaining way to explain how applied mathematics and engineering work together to solve problems, everything from keeping a piston aligned in its cylinder to ensuring that automotive driveshafts rotate smoothly. Intriguingly, checking the roundness of a manufactured object is trickier than one might think. When does the width of a saw blade affect an engineer's calculations--or, for that matter, the width of a physical line? When does a measurement need to be exact and when will an approximation suffice? Bryant and Sangwin tackle questions like these and enliven their discussions with many fascinating highlights from engineering history. Generously illustrated, How Round Is Your Circle? reveals some of the hidden complexities in everyday things.

Analytical Conics

Author: Barry Spain

Publisher: Courier Corporation

ISBN: 0486457737

Category: Mathematics

Page: 145

View: 8578

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This concise text introduces students to analytical geometry, covering basic ideas and methods. Readily intelligible to any student with a sound mathematical background, it is designed both for undergraduates and for math majors. It will prove particularly valuable in preparing readers for more advanced treatments. The text begins with an overview of the analytical geometry of the straight line, circle, and the conics in their standard forms. It proceeds to discussions of translations and rotations of axes, and of the general equation of the second degree. The concept of the line at infinity is introduced, and the main properties of conics and pencils of conics are derived from the general equation. The fundamentals of cross-ratio, homographic correspondence, and line-coordinates are explored, including applications of the latter to focal properties. The final chapter provides a compact account of generalized homogeneous coordinates, and a helpful appendix presents solutions to many of the examples.

Geometry of Linear 2-normed Spaces

Author: Raymond W. Freese,Yeol Je Cho

Publisher: Nova Publishers

ISBN: 9781590330197

Category: Mathematics

Page: 301

View: 6027

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To encourage researchers in mathematics to apply metric geometry, functional analysis, and topology, Freese and Cho, who are not identified, introduce 2-metric spaces and linear 2 normed spaces. They survey recent results on the relations between linear 2-normed spaces and normed linear spaces, the completion of linear 2-normed spaced, 2-inner spaces, 2-inner product spaces, strict convexity, strict 2-convexity, uniform convexity, isometry conditions, orthogonal relations, quadratic forms, and other topics. c. Book News Inc.

The Last Recreations

Hydras, Eggs, and Other Mathematical Mystifications

Author: Martin Gardner

Publisher: Springer Science & Business Media

ISBN: 0387258272

Category: Mathematics

Page: 392

View: 9307

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Of all of Martin Gardners writings, none gained him a wider audience or was more central to his reputation than his Mathematical Recreations column in Scientific American - which virtually defined the genre of popular mathematics writing for a generation. Flatland, Hydras and Eggs: Mathematical Mystifications is the final collection of these columns, covering the period roughly from 1979 to Gardners retirement in 1986. As always in his published collections, Gardner includes letters commenting on the ideas presented in his articles. These columns show him at the top of his form and should not be missed by anyone with an interest in mathematics.

Practical Conic Sections

The Geometric Properties of Ellipses, Parabolas and Hyperbolas

Author: J. W. Downs

Publisher: Courier Corporation

ISBN: 0486148882

Category: Mathematics

Page: 112

View: 2077

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Using examples from everyday life, this text studies ellipses, parabolas, and hyperbolas. Explores their ancient origins and describes the reflective properties and roles of curves in design applications. 1993 edition. Includes 98 figures.

Making Geometry Come Alive

Student Activities and Teacher Notes

Author: Alfred S. Posamentier

Publisher: Corwin Press

ISBN: 9780761975991

Category: Education

Page: 163

View: 6197

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All the basics of geometry in a motivating new format, from Ptolemy to Napoleon, from the Arbelos to the billiard table!

Euclidean and Transformational Geometry: A Deductive Inquiry

Author: Shlomo Libeskind

Publisher: Jones & Bartlett Publishers

ISBN: 1449650090

Category: Mathematics

Page: 371

View: 330

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Ideal for mathematics majors and prospective secondary school teachers, Euclidean and Transformational Geometry provides a complete and solid presentation of Euclidean geometry with an emphasis on solving challenging problems. The author examines various strategies and heuristics for approaching proofs and discusses the process students should follow to determine how to proceed from one step to the next through numerous problem solving techniques. A large collection of problems, varying in level of difficulty, are integrated throughout the text and suggested hints for the more challenging problems appear in the instructor's solutions manual and can be used at the instructor's discretion.

Introduction To Non-Euclidean Geometry

Author: Harold E. Wolfe

Publisher: Read Books Ltd

ISBN: 1446547302

Category: Science

Page: 260

View: 7487

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Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

Adventures in Dynamic Geometry

Author: Gerry Stahl

Publisher: Lulu.com

ISBN: 1329859634

Category: Education

Page: 352

View: 6131

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Math games and workbooks with topics for online small groups of teachers or students to collaboratively learn dynamic geometry. The approach is based on -Translating Euclid.- The many GeoGebra files used in VMT courses are pictured in the workbook. Several versions of the workbooks are available, including the version used in WinterFest 2013 and analyzed in -Translating Euclid- and -Constructing Dynamic Triangles Together.- Also includes the content of a game version that is available as a GeoGebraBook.

Geometry and Symmetry

Author: L. Christine Kinsey,Teresa E. Moore,Efstratios Prassidis

Publisher: John Wiley & Sons

ISBN: 0470499494

Category: Mathematics

Page: 459

View: 6533

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This new book helps students gain an appreciation of geometry and its importance in the history and development of mathematics. The material is presented in three parts. The first is devoted to Euclidean geometry. The second covers non-Euclidean geometry. The last part explores symmetry. Exercises and activities are interwoven with the text to enable them to explore geometry. The activities take advantage of geometric software so they'll gain a better understanding of its capabilities. Mathematics teachers will be able to use this material to create exciting and engaging projects in the classroom.