This comprehensive, best-selling text focuses on the study of many different geometries--rather than a single geometry--and emphasizes practical applications. Designed to be a flexible teaching tool for a wide range of students (including math, education, or computer science majors), Smart's text features self-contained chapters organized so that instructors can cover as much or as little of each topic as they choose, from bare minimum one-section coverage to full-chapter coverage. Modern Geometries has earned a reputation for its logical progression of ideas, its well-constructed exercises, and its comprehensive coverage. In this edition, Smart covers the major new applied areas of computer graphics, and emphasizes matrices for transformations.
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1. SETS OF AXIOMS AND FINITE GEOMETRIES Introduction to Geometry / Development of Modern Geometries / Introduction to Finite Geometries / Four-Line and Four-Point Geometries / Finite Geometries of Fano and Young / Finite Geometries of Pappus and Desargues / Other Finite Geometries 2. GEOMETRIC TRANSFORMATIONS Introduction to Transformations / Groups of Transformations / Euclidean Motions of the Plane / Sets of Equations for Motions of the Plane / Applications of Transformations in Computer Graphics / Properties of the Group of Euclidean Motions / Motions and Graphics of Three-Space / Similarity Transformations / Introduction to the Geometry of Fractals and Fractal Dimension / Examples and Applications of Fractals 3. CONVEXITY Basic Concepts / Convex Sets and Supporting Lines / Convex Bodies in Two-Space / Convex Bodies in Three-Space / Convex Hulls / Width of a Set / Helly's Theorem and Applications 4. MODERN EUCLIDEAN GEOMETRY, THEORY, AND APPLICATIONS Fundamental Concepts and Theorems / Some Theorems Leading to Modern Synthetic Geometry / The Nine-Point Circle and Early Nineteenth-Century Synthetic Geometry / Isogonal Conjugates / Recent Synthetic Geometry of the Triangle / Golden Ratio, Tessellations, Packing Problems and Pick's Theorem / Extremum Problems, Geometric Probability, Fuzzy Sets, and Bezier Curves 5. CONSTRUCTIONS The Philosophy of Constructions / Constructible Numbers / Constructions in Advanced Euclidean Geometry / Constructions and Impossibility Proofs / Constructions by Paper Folding and by Use of Computer Software / Constructions with Only One Instrument 6. THE TRANSFORMATION OF INVERSION Basic Concepts / Additional Properties and Invariants under Inversion / The Analytic Geometry of Inversion / Some Applications of Inversion 7. PROJECTIVE GEOMETRY Fundamental Concepts / Postulational Basis for Projective Geometry / Duality and Some Consequences / Harmonic Sets / Projective Transformations / Homogenous Coordinates / Equations for Projective Transformations / Special Projectivities / Conics / Constructions of Conics 8. GEOMETRIC INTRODUCTION TO TOPOLOGICAL TRANSFORMATIONS Topological Transformations / Simple Closed Curves / Invariant Points and Networks / Introduction to the Topology of Surfaces / Euler's Formula and the Map-Coloring Problem 9. NON-EUCLIDEAN GEOMETRIES Foundations of Euclidean and Non-Euclidean Geometries / Introduction to Hyperbolic Geometry / Ideal Points and Omega Triangles / Quadrilaterals and Triangles / Pairs of Lines and Area of Triangular Regions / Curves / Elliptic Geometry / Consistency; Other Modern Geometries / APPENDIX 1: SELECTED IDEAS FROM LOGIC / APPENDIX 2: REVIEW OF EUCLIDEAN GEOMETRY / APPENDIX 3: FIRST TWENTY-EIGHT PROPOSITIONS OF EUCLID / APPENDIX 4: HILBERT'S AXIOMS / APPENDIX 5: BIRKHOFF'S POSTULATES / APPENDIX 6: ILLUSTRATIONS OF BASIC EUCLIDEAN CONSTRUCTIONS / BIBLIOGRAPHY / ANSWERS TO SELECTED EXERCISES / INDEX
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Book Description Brooks/Cole Pub. Co, 1973. Book Condition: Good. Former Library book. Shows some signs of wear, and may have some markings on the inside. Bookseller Inventory # GRP9640425
Book Description Brooks/Cole Pub. Co, 1973. Book Condition: Very Good. Former Library book. Great condition for a used book! Minimal wear. Bookseller Inventory # GRP73662720
Book Description Brooks/Cole Pub. Co, 1973. Hardcover. Book Condition: Very Good. Publisher: Brooks/Cole Pub Co, Date of Publication: 1973, Binding: hardcover without DJ, Condition: Very Good. 0818500514. Bookseller Inventory # 008248
Book Description Brooks/Cole Pub. Co, 1973. Book Condition: Very Good. Ships from the UK. Former Library book. Great condition for a used book! Minimal wear. Bookseller Inventory # GRP96903165
Book Description Brooks/Cole Pub. Co 1973-01, 1973. Hardcover. Book Condition: Good. Signature to the inside cover. Some dirt marks to the face on both sides. Clean and readable inside, a decent hardback formerly owned. Bookseller Inventory # 130244-3
Book Description Book Condition: Good. Modern geometries (Contemporary undergraduate mathematics series). Bookseller Inventory # SKU0460101
Book Description Brooks/Cole Pub. Co, 1973. Hardcover. Book Condition: Good. Ships with Tracking Number! INTERNATIONAL WORLDWIDE Shipping available. May not contain Access Codes or Supplements. Buy with confidence, excellent customer service!. Bookseller Inventory # 0818500514
Book Description Florence, Kentucky, U.S.A.: Brooks/Cole Pub Co, Florence, Kentucky, U.S.A., 1973. Hardcover. Book Condition: Good. No Jacket. 1st Edition. Unmarked copy of first printing. Ex-library from the University of Wisconsin at LaCrosse. Bookseller Inventory # 00512