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Taxicab Geometry

Taxicab Geometry

An Adventure in Non-Euclidean Geometry

  • Author: Eugene F. Krause
  • Publisher: Courier Corporation
  • ISBN: 048613606X
  • Category: Mathematics
  • Page: 96
  • View: 749
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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.

Advanced Euclidean Geometry

Advanced Euclidean Geometry

  • Author: Roger A. Johnson
  • Publisher: Courier Corporation
  • ISBN: 048615498X
  • Category: Mathematics
  • Page: 336
  • View: 6583
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This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.

Introduction To Non-Euclidean Geometry

Introduction To Non-Euclidean Geometry

  • Author: Harold E. Wolfe
  • Publisher: Read Books Ltd
  • ISBN: 1446547302
  • Category: Science
  • Page: 260
  • View: 7074
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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.

Analytical Conics

Analytical Conics

  • Author: Barry Spain
  • Publisher: Courier Corporation
  • ISBN: 0486457737
  • Category: Mathematics
  • Page: 145
  • View: 6435
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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.

How Round Is Your Circle?

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: 3945
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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.

Practical Conic Sections

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: 6388
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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.

Geometry, Relativity and the Fourth Dimension

Geometry, Relativity and the Fourth Dimension

  • Author: Rudolf Rucker
  • Publisher: Courier Corporation
  • ISBN: 0486140334
  • Category: Science
  • Page: 160
  • View: 6953
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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.

Taxicab geometry

Taxicab geometry

  • Author: Eugene F. Krause
  • Publisher: Addison Wesley Publishing Company
  • ISBN: N.A
  • Category: Juvenile Nonfiction
  • Page: 88
  • View: 9567
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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.

Euclidean Geometry and Transformations

Euclidean Geometry and Transformations

  • Author: Clayton W. Dodge
  • Publisher: Courier Corporation
  • ISBN: 0486138429
  • Category: Mathematics
  • Page: 304
  • View: 2500
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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.

Lectures on Analytic and Projective Geometry

Lectures on Analytic and Projective Geometry

  • Author: Dirk J. Struik
  • Publisher: Courier Corporation
  • ISBN: 0486173526
  • Category: Mathematics
  • Page: 304
  • View: 2867
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This undergraduate text develops the geometry of plane and space, leading up to conics and quadrics, within the context of metrical, affine, and projective transformations. 1953 edition.

A New Look at Geometry

A New Look at Geometry

  • Author: Irving Adler
  • Publisher: Courier Corporation
  • ISBN: 0486320499
  • Category: Mathematics
  • Page: 416
  • View: 7930
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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.

Problems and Solutions in Euclidean Geometry

Problems and Solutions in Euclidean Geometry

  • Author: M. N. Aref,William Wernick
  • Publisher: Courier Corporation
  • ISBN: 0486477207
  • Category: Mathematics
  • Page: 258
  • View: 8224
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Based on classical principles, this book is intended for a second course in Euclidean geometry and can be used as a refresher. Each chapter covers a different aspect of Euclidean geometry, lists relevant theorems and corollaries, and states and proves many propositions. Includes more than 200 problems, hints, and solutions. 1968 edition.

Methods of Applied Mathematics

Methods of Applied Mathematics

  • Author: Francis B. Hildebrand
  • Publisher: Courier Corporation
  • ISBN: 0486138380
  • Category: Science
  • Page: 362
  • View: 3751
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Offering a number of mathematical facts and techniques not commonly treated in courses in advanced calculus, this book explores linear algebraic equations, quadratic and Hermitian forms, the calculus of variations, more.

Ruler and the Round

Ruler and the Round

Classic Problems in Geometric Constructions

  • Author: Nicholas D. Kazarinoff
  • Publisher: Courier Corporation
  • ISBN: 0486143619
  • Category: Mathematics
  • Page: 160
  • View: 5850
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An intriguing look at the "impossible" geometric constructions (those that defy completion with just a ruler and a compass), this book covers angle trisection and circle division. 1970 edition.

Fundamental Concepts of Geometry

Fundamental Concepts of Geometry

  • Author: Bruce E. Meserve
  • Publisher: Courier Corporation
  • ISBN: 048615226X
  • Category: Mathematics
  • Page: 336
  • View: 564
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Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.

Geometry from Euclid to Knots

Geometry from Euclid to Knots

  • Author: Saul Stahl
  • Publisher: Courier Corporation
  • ISBN: 0486134989
  • Category: Mathematics
  • Page: 480
  • View: 1601
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This text provides a historical perspective on plane geometry and covers non-neutral Euclidean geometry, circles and regular polygons, projective geometry, symmetries, inversions, informal topology, and more. Includes 1,000 practice problems. Solutions available. 2003 edition.

Mathematics and the Imagination

Mathematics and the Imagination

  • Author: Edward Kasner,James Newman
  • Publisher: Courier Corporation
  • ISBN: 0486320278
  • Category: Mathematics
  • Page: 400
  • View: 4167
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With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.

Flatland

Flatland

A Romance of Many Dimensions

  • Author: Edwin Abbott Abbott
  • Publisher: N.A
  • ISBN: N.A
  • Category: FICTION
  • Page: 102
  • View: 9066
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Considered both a satire and a science fiction novella, Abbott's Flatland experiments with the idea of various dimensions in time and space.

Geometry and the Visual Arts

Geometry and the Visual Arts

  • Author: Daniel Pedoe
  • Publisher: Courier Corporation
  • ISBN: 9780486244587
  • Category: Mathematics
  • Page: 296
  • View: 8991
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This survey traces the effects of geometry on artistic achievement and clearly discusses its importance to artists and scientists. It also surveys projective geometry, mathematical curves, theories of perspective, architectural form, and concepts of space.

Excursions in Geometry

Excursions in Geometry

  • Author: Charles Stanley Ogilvy
  • Publisher: Courier Corporation
  • ISBN: 0486265307
  • Category: Mathematics
  • Page: 178
  • View: 1281
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A straightedge, compass, and a little thought are all that's needed to discover the intellectual excitement of geometry. Harmonic division and Apollonian circles, inversive geometry, hexlet, Golden Section, more. 132 illustrations.