Geometry and its applications / Walter Meyer.

Format:

Book

Author/Creator:

Meyer, Walter J. (Walter Joseph), 1943-

Language:

English

Subjects (All):

Geometry--Textbooks.

Geometry.

Physical Description:

1 online resource (560 p.)

Edition:

2nd ed.

Place of Publication:

Burlington, MA : Elsevier Academic Press, c2006.

Language Note:

English

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 use

Contents:

Preface; Introduction; Axiomatic Geometry; Rigidity and Architecture; Computer Graphics; Symmetries in Anthropology; Robotics; Molecular Shapes; 1 The Axiomatic Method in Geometry; 1.1 The Aims of Axiomatic Geometry; Section 1.1 Exercises; 1.2 Proofs in Axiomatic Geometry; Section 1.2 Exercises; 1.3 Axioms for Euclidean Geometry; Section 1.3 Exercises; 2 The Euclidean Heritage; 2.1 Congruence; Section 2.1 Exercises; 2.2 Perpendicularity; Section 2.2 Exercises; 2.3 Parallelism; Section 2.3 Exercises; 2.4 Area and Similarity; Section 2.4 Exercises; 3 Non-Euclidean Geometry

3.1 Hyperbolic and Other Non-Euclidean GeometriesSection 3.1 Exercises; 3.2 Spherical Geometry: A Three-Dimensional View; Section 3.2 Exercises; 3.3 Spherical Geometry: An Axiomatic View; Section 3.3 Exercises; 4 Transformation Geometry I: Isometries and Symmetries; 4.1 Isometries and Their Invariants; Section 4.1 Exercises; 4.2 Composing Isometries; Section 4.2 Exercises; 4.3 There Are Only Four Kinds of Isometries; Section 4.3 Exercises; 4.4 Symmetries of Patterns; Section 4.4 Exercises; 4.5 What Combinations of Symmetries Can Strip Patterns Have?; Section 4.5 Exercises

5 Vectors in Geometry5.1 Parametric Equations of Lines; Section 5.1 Exercises; 5.2 Scalar Products, Planes, and the Hidden Surface Problem; Section 5.2 Exercises; 5.3 Norms, Spheres, and the Global Positioning System; Section 5.3 Exercises; 5.4 Curve Fitting with Splines in Two Dimensions; Section 5.4 Exercises; 6 Transformation Geometry II: Isometries and Matrices; 6.1 Equations and Matrices for Familiar Transformations; Section 6.1 Exercises; 6.2 Composition and Matrix Multiplication; Section 6.2 Exercises; 6.3 Frames and How to Represent Them; Section 6.3 Exercises

6.4 Properties of the Frame MatrixSection 6.4 Exercises; 6.5 Forward Kinematics for a Simple Robot Arm; Section 6.5 Exercises; 7 Transformation Geometry III: Similarity, Inversion, and Projection; 7.1 Central Similarity and Other Similarity Transformations in the Plane; Section 7.1 Exercises; 7.2 Inversion; Section 7.2 Exercises; 7.3 Perspective Projection and Image Formation; Section 7.3 Exercises; 7.4 Parallelism and Vanishing Points of a Perspective Projection; Section 7.4 Exercises; 7.5 Parallel Projection; Section 7.5 Exercises; 8 Graphs, Maps, and Polyhedra

8.1 Introduction to Graph TheorySection 8.1 Exercises; 8.2 Euler's Formula and the Euler Number; Section 8.2 Exercises; 8.3 Polyhedra, Combinatorial Structure, and Planar Maps; Section 8.3 Exercises; 8.4 Special Kinds of Polyhedra: Regular Polyhedra and Fullerenes; Section 8.4 Exercises; 8.5 List Coloring and the Five-Color Theorem; Section 8.5 Exercises; Bibliography; Chapters 1 and 2; Chapter 3; Chapter 4; Chapter 5; Chapter 6; Chapter 7; Chapter 8; Answers to Odd-Numbered Exercises; Chapter 1; Chapter 2; Chapter 3; Chapter 4; Chapter 5; Chapter 6; Chapter 7; Chapter 8; Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 459-461) and index.

ISBN:

9786611050528

9781281050526

1281050520

9780080478036

0080478034

OCLC:

469499431