Geometry And Its Applications,9780123694270

Geometry And Its Applications

by
Edition: 2nd
ISBN13: 9780123694270
ISBN10: 0123694272
Format: Hardcover
Pub. Date: 2006-02-21
Publisher(s): Elsevier Science
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Summary

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 * Instructor's Manual with solutions available for all adopters of the text

Table of Contents

Preface ix
Introduction xiii
The Axiomatic Method in Geometry
1(36)
Section 1 The Aims of Axiomatic Geometry
1(10)
Applied Topic: Scan-Converting a Line Segment
Section 2 Proofs in Axiomatic Geometry
11(9)
Section 3 Axioms for Euclidean Geometry
20(17)
The Euclidean Heritage
37(66)
Section 1 Congruence
37(14)
Applied Topics The Carpenter's Level. Distance Estimation
Section 2 Perpendicularity
51(17)
Applied Topic: Fermat's Least Time Principle
Section 3 Parallelism
68(19)
Applied Topics: The Circumference of the Earth, Stability of Frameworks
Section 4 Area and Similarity
87(16)
Non-Euclidean Geometry
103(40)
Section 1 Hyperbolic and Other Non-Euclidean Geometries
103(13)
Applied Topic: Astronomy
Section 2 Spherical Geometry: A Three-Dimensional View
116(13)
Applied Topic Map Making
Section 3 Spherical Geometry: An Axiomatic View
129(14)
Transformation Geometry I: Isometries and Symmetries
143(56)
Applied Topic: Analyzing Symmetries of Strip Patterns
Section 1 Isometries and Their Invariants
143(12)
Section 2 Composing Isometries
155(14)
Section 3 There Are Only Four Kinds of Isometries
169(12)
Section 4 Symmetries of Patterns
181(11)
Section 5 What Combinations of Symmetries Can Strip Patterns Have?
192(7)
Vectors in Geometry
199(58)
Section 1 Parametric Equations of Lines
199(19)
Applied Topics: Robotics, Computer Graphics, Stereo Vision
Section 2 Scalar Products, Planes, and the Hidden Surface Problem
218(13)
Applied Topic: Three-Dimensional Computer Graphics
Section 3 Norms, Spheres, and the Global Positioning System
231(11)
Applied Topics: Cartography, Navigation
Section 4 Curve Fitting with Splines in Two Dimensions
242(15)
Applied Topics: Engineering and Commercial Art
Transformation Geometry II: Isometries and Matrices
257(54)
Section 1 Equations and Matrices for Familiar Transformations
258(11)
Applied Topic: Computer Graphics
Section 2 Composition and Matrix Multiplication
269(9)
Applied Topics: CAD/CAM. Robotics
Section 3 Frames and How to Represent Them
278(10)
Applied Topics: CAD/CAM, Robotics
Section 4 Properties of the Frame Matrix
288(9)
Applied Topics: CAD/CAM, Robotics
Section 5 Forward Kinematics for a Simple Robot Arm
297(14)
Transformation Geometry III: Similarity, Inversion, and Projection
311(68)
Section 1 Central Similarity and Other Similarity Transformations in the Plane
312(10)
Applied Topic: Zooming In and Out in Computer Graphics
Section 2 Inversion
322(12)
Applied Topics: Mechanical Engineering, Cartography
Section 3 Perspective Projection and Image Formation
334(14)
Applied Topics: Art and Computer Graphics
Section 4 Parallelism and Vanishing Points of a Perspective Projection
348(14)
Applied Topics: Art and Computer Graphics
Section 5 Parallel Projection
362(17)
Applied Topics: Art and Computer Graphics
Graphs, Maps, and Polyhedra
379(80)
Section 1 Introduction to Graph Theory
379(25)
Applied Topics: Chemistry, Chip Design, Scheduling
Section 2 Euler's Formula and the Euler Number
404(13)
Applied Topic: Computer Vision
Section 3 Polyhedra, Combinatorial Structure, and Planar Maps
417(15)
Section 4 Special Kinds of Polyhedra: Regular Polyhedra and Fullerenes
432(12)
Applied Topic: Buckyballs and Fullerenes in Chemistry
Section 5 List Coloring and the Five-Color Theorem
444(15)
Applied Topic: Scheduling
Bibliography 459(4)
Answers to Odd-Numbered Exercises 463(60)
Index 523

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