College Geometry A Discovery Approach 2nd edition By David Kay – Ebook PDF Instant Download/Delivery: 0321046242, 978-0321046246
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ISBN 10: 0321046242
ISBN 13: 978-0321046246
Author: David Kay
College Geometry is an approachable text, covering both Euclidean and Non-Euclidean geometry. This text is directed at the one semester course at the college level, for both pure mathematics majors and prospective teachers. A primary focus is on student participation, which is promoted in two ways: (1) Each section of the book contains one or two units, called Moments for Discovery, that use drawing, computational, or reasoning experiments to guide students to an often surprising conclusion related to section concepts; and (2) More than 650 problems were carefully designed to maintain student interest.
College Geometry A Discovery Approach 2nd Table of contents:
CHAPTER ONE: Exploring Geometry
Overview
1.1 Discovery in Geometry
*1.2 Variations on Two Familiar Geometric Themes
1.3 Discovery via the Computer
*1.4 Steiner’s Theorem
CHAPTER TWO: Foundations of Geometry 1: Points, Lines, Segments, Angles
Overview
*2.1 An Introduction to Axiomatics and Proof
*2.2 The Role of Examples and Models
2.3 Incidence Axioms for Geometry
2.4 Distance, Ruler Postulate, Segments, Rays, and Angles
2.5 Angle Measure and the Protractor Postulate
*2.6 Plane Separation, Interior of Angles, Crossbar Theorem
CHAPTER SUMMARY
TESTING YOUR KNOWLEDGE
CHAPTER THREE: Foundations of Geometry 2: Triangles, Quadrilaterals, Circles
Overview
3.1 Triangles, Congruence Relations, SAS Hypothesis
*3.2 Taxicab Geometry: Geometry without SAS Congruence
3.3 SAS, ASA, SSS Congruence, and Perpendicular Bisectors
3.4 Exterior Angle Inequality
3.5 The Inequality Theorems
3.6 Additional Congruence Criteria
3.7 Quadrilaterals
3.8 Circles
CHAPTER SUMMARY
TESTING YOUR KNOWLEDGE
CHAPTER 4 Euclidean Geometry: Trigonometry, Coordinates and Vectors
Overview
4.1 Euclidean Parallelism, Existence of Rectangles
4.2 Parallelograms and Trapezoids: Parallel Projection
4.3 Similar Triangles, Pythagorean Theorem, Trigonometry
4.4 Regular Polygons and Tiling
4.5 The Circle Theorems
*4.6 Euclid’s Concept of Area and Volume
*4.7 Coordinate Geometry and Vectors
*4.8 Some Modern Geometry of the Triangle
CHAPTER SUMMARY
TESTING YOUR KNOWLEDGE
CHAPTER 5 Transformations in Geometry
Overview
*5.1 Euclid’s Superposition Proof and Plane Transformations
5.2 Reflections: Building Blocks for Isometries
5.3 Translations, Rotations, and Other Isometries
5.4 Other Linear Transformations
5.5 Coordinate Characterizations
*5.6 Transformation Groups
*5.7 Using Transformation Theory in Proofs
CHAPTER SUMMARY
TESTING YOUR KNOWLEDGE
CHAPTER 6 Alternate Concepts for Parallelism: Non-Euclidean Geometry
Overview
6.1 Historical Background of Non-Euclidean Geometry
6.2 An Improbable Logical Case
6.3 Hyperbolic Geometry: Angle Sum Theorem
*6.4 Two Models for Hyperbolic Geometry
*6.5 Circular Inversion: Proof of SAS Postulate for Half-Plane Model
CHAPTER SUMMARY
TESTING YOUR KNOWLEDGE
CHAPTER 7 An Introduction to Three-Dimensional Geometry
Overview
7.1 Orthogonality Concepts for Lines and Planes
7.2 Parallelism in Space: Prisms, Pyramids, and the Platonic Solids
7.3 Cones, Cylinders, and Spheres
7.4 Volume in E[sup(3)]
*7.5 Coordinates, Vectors, and Isometries in E[sup(3)]
*7.6 Spherical Geometry
CHAPTER SUMMARY
TESTING YOUR KNOWLEDGE
Appendixes
Appendix A: Bibliography
Appendix B: Review of Topics in Secondary School Geometry
Appendix C: The Geometer’s Sketchpad: Brief Instructions
Appendix D: Unified Axiom System for the Three Classical Geometries
Appendix E: Answers to Selected Problems
Appendix F: Symbols, Definitions, Axioms, Theorems, and Corollaries
Index
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