Taxicab Geometry

An Adventure in Non-Euclidean Geometry
Author: Eugene F. Krause
Publisher: Courier Corporation
ISBN: 048613606X
Category: Mathematics
Page: 96
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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.

Introduction To Non-Euclidean Geometry


Author: Harold E. Wolfe
Publisher: Read Books Ltd
ISBN: 1446547302
Category: Science
Page: 260
View: 6987

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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.

Advanced Euclidean Geometry


Author: Roger A. Johnson
Publisher: Courier Corporation
ISBN: 048615498X
Category: Mathematics
Page: 336
View: 6895

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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.

Geometry, Relativity and the Fourth Dimension


Author: Rudolf Rucker
Publisher: Courier Corporation
ISBN: 0486140334
Category: Science
Page: 160
View: 3457

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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.

Analytical Conics


Author: Barry Spain
Publisher: Courier Corporation
ISBN: 0486457737
Category: Mathematics
Page: 145
View: 3353

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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.

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: 321

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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.

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: 9770

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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.

A Vector Space Approach to Geometry


Author: Melvin Hausner
Publisher: Courier Corporation
ISBN: 0486137856
Category: Mathematics
Page: 416
View: 2004

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This examination of geometry's correlation with other branches of math and science features a review of systematic geometric motivations in vector space theory and matrix theory; more. 1965 edition.

Euclidean Geometry and Transformations


Author: Clayton W. Dodge
Publisher: Courier Corporation
ISBN: 0486138429
Category: Mathematics
Page: 304
View: 1527

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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.

A New Look at Geometry


Author: Irving Adler
Publisher: Courier Corporation
ISBN: 0486320499
Category: Mathematics
Page: 416
View: 6812

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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.

Lectures on Analytic and Projective Geometry


Author: Dirk J. Struik
Publisher: Courier Corporation
ISBN: 0486173526
Category: Mathematics
Page: 304
View: 9393

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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.

Methods of Applied Mathematics


Author: Francis B. Hildebrand
Publisher: Courier Corporation
ISBN: 0486138380
Category: Science
Page: 362
View: 497

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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.

An Imaginary Tale

The Story of √-1
Author: Paul J. Nahin
Publisher: Princeton University Press
ISBN: 9781400833894
Category: Mathematics
Page: 296
View: 2281

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Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions.

Geometry from Euclid to Knots


Author: Saul Stahl
Publisher: Courier Corporation
ISBN: 0486134989
Category: Mathematics
Page: 480
View: 4816

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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.

Ruler and the Round

Classic Problems in Geometric Constructions
Author: Nicholas D. Kazarinoff
Publisher: Courier Corporation
ISBN: 0486143619
Category: Mathematics
Page: 160
View: 3446

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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


Author: Bruce E. Meserve
Publisher: Courier Corporation
ISBN: 048615226X
Category: Mathematics
Page: 336
View: 3544

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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.

Mathematics and the Imagination


Author: Edward Kasner,James Newman
Publisher: Courier Corporation
ISBN: 0486320278
Category: Mathematics
Page: 400
View: 5627

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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.

Problems and Solutions in Euclidean Geometry


Author: M. N. Aref,William Wernick
Publisher: Courier Corporation
ISBN: 0486477207
Category: Mathematics
Page: 258
View: 9344

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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.

Connections

The Geometric Bridge Between Art and Science
Author: Jay Kappraff
Publisher: World Scientific
ISBN: 9789812811394
Category: Science
Page: 486
View: 6869

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The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in OC Mathematics, Chemistry, and Astronomy OCo Professional and ReferenceOCO in 1991. It has been a comprehensive reference in design science, bringing together in a single volume material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry. The book presents both theory and practice and has more than 750 illustrations. It is suitable for research in a variety of fields and as an aid to teaching a course in the mathematics of design. It has been influential in stimulating the burgeoning interest in the relationship between mathematics and design. In the second edition there are five new sections, supplementary, as well as a new preface describing the advances in design science since the publication of the first edition. Contents: Proportion in Architecture; Similarity; The Golden Mean; Graphs; Tilings with Polygons; Two-Dimensional Networks and Lattices; Polyhedra: Platonic Solids; Transformation of the Platonic Solids I; Transformation of the Platonic Solids II; Polyhedra: Space Filling; Isometries and Mirrors; Symmetry of the Plane. Readership: Polytechnic students, architects, designers, mathematicians and general readers."

Geometry and the Visual Arts


Author: Daniel Pedoe
Publisher: Courier Corporation
ISBN: 9780486244587
Category: Mathematics
Page: 296
View: 8054

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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.