Format:
1 online resource (560 pages)
Edition:
2nd ed.
ISBN:
9780080478036
Content:
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.
Content:
Intro -- 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 Geometries -- Section 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 Geometry -- 5.1 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.
Note:
Description based on publisher supplied metadata and other sources
Additional Edition:
9780123694270
Additional Edition:
Erscheint auch als Druck-Ausgabe Meyer, Walter J. Geometry and its applications Amsterdam [u.a.] : Elsevier Academic Press, 2006 0123694272
Additional Edition:
9780123694270
Language:
English
Subjects:
Mathematics
Keywords:
Geometrie
URL:
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