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College Geometry : A Discovery Approach,9780321046246
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College Geometry : A Discovery Approach

by
Edition:
2nd
ISBN13:

9780321046246

ISBN10:
0321046242
Format:
Paperback
Pub. Date:
11/15/2000
Publisher(s):
Pearson
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This is the 2nd edition with a publication date of 11/15/2000.
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  • College Geometry : A Discovery Approach
    College Geometry : A Discovery Approach




Summary

College Geometryis 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 M oments 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.

Table of Contents

Preface ix
To the Student xvii
Exploring Geometry
1(50)
Overview
1(1)
Discovery in Geometry
2(12)
Variations on Two Familiar Geometric Themes
14(13)
Discovery via the Computer
27(12)
Steiner's Theorem
39(12)
Foundations of Geometry 1: Points, Lines, Segments, Angles
51(68)
Overview
51(1)
An Introduction to Axiomatics and Proof
52(10)
The Role of Examples and Models
62(8)
Incidence Axioms for Geometry
70(7)
Distance, Ruler Postulate, Segments, Rays, and Angles
77(13)
Angle Measure and the Protractor Postulate
90(13)
Plane Separation, Interior of Angles, Crossbar Theorem
103(16)
Chapter Summary
116(1)
Testing Your Knowledge
117(2)
Foundations of Geometry 2: Triangles, Quadrilaterals, Circles
119(92)
Overview
119(1)
Triangles, Congruence Relations, SAS Hypothesis
120(7)
Taxicab Geometry: Geometry without SAS Congruence
127(12)
SAS, ASA, SSS Congruence, and Perpendicular Bisectors
139(13)
Exterior Angle Inequality
152(14)
The Inequality Theorems
166(8)
Additional Congruence Criteria
174(9)
Quadrilaterals
183(11)
Circles
194(17)
Chapter Summary
208(1)
Testing Your Knowledge
209(2)
Euclidean Geometry: Trigonometry, Coordinates and Vectors
211(120)
Overview
211(1)
Euclidean Parallelism, Existence of Rectangles
211(13)
Parallelograms and Trapezoids: Parallel Projection
224(12)
Similar Triangles, Pythagorean Theorem, Trigonometry
236(18)
Regular Polygons and Tiling
254(15)
The Circle Theorems
269(15)
Euclid's Concept of Area and Volume
284(17)
Coordinate Geometry and Vectors
301(14)
Some Modern Geometry of the Triangle
315(16)
Chapter Summary
328(1)
Testing Your Knowledge
329(2)
Transformations in Geometry
331(90)
Overview
331(1)
Euclid's Superposition Proof and Plane Transformations
331(10)
Reflections: Building Blocks for Isometries
341(12)
Translations, Rotations, and Other Isometries
353(9)
Other Linear Transformations
362(11)
Coordinate Characterizations
373(16)
Transformation Groups
389(13)
Using Transformation Theory in Proofs
402(19)
Chapter Summary
418(1)
Testing Your Knowledge
419(2)
Alternate Concepts for Parallelism: Non-Euclidean Geometry
421(72)
Overview
421(1)
Historical Background of Non-Euclidean Geometry
421(4)
An Improbable Logical Case
425(11)
Hyperbolic Geometry: Angle Sum Theorem
436(9)
Two Models for Hyperbolic Geometry
445(24)
Circular Inversion: Proof of SAS Postulate for Half-Plane Model
469(24)
Chapter Summary
489(1)
Testing Your Knowledge
490(3)
An Introduction to Three-Dimensional Geometry
493(67)
Overview
493(1)
Orthogonality Concepts for Lines and Planes
493(10)
Parallelism in Space: Prisms, Pyramids, and the Platonic Solids
503(11)
Cones, Cylinders, and Spheres
514(8)
Volume in E3
522(10)
Coordinates, Vectors, and Isometries in E3
532(13)
Spherical Geometry
545(15)
Chapter Summary
559(1)
Testing Your Knowledge
560
Appendixes
Appendix A Bibliography
A-1
Appendix B Review of Topics in Secondary School Geometry
A-2
Appendix C The Geometer's Sketchpad: Brief Instructions
A-27
Appendix D Unified Axiom System for the Three Classical Geometries
A-31
Appendix E Answers to Selected Problems
A-35
Appendix F Symbols, Definitions, Axioms, Theorems, and Corollaries
A-55
Index I-1


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