What is included with this book?
Preface | p. ix |
To the Student | p. xvii |
Exploring Geometry | p. 1 |
Overview | p. 1 |
Discovery in Geometry | p. 2 |
Variations on Two Familiar Geometric Themes | p. 14 |
Discovery via the Computer | p. 27 |
Steiner's Theorem | p. 39 |
Foundations of Geometry 1: Points, Lines, Segments, Angles | p. 51 |
Overview | p. 51 |
An Introduction to Axiomatics and Proof | p. 52 |
The Role of Examples and Models | p. 62 |
Incidence Axioms for Geometry | p. 70 |
Distance, Ruler Postulate, Segments, Rays, and Angles | p. 77 |
Angle Measure and the Protractor Postulate | p. 90 |
Plane Separation, Interior of Angles, Crossbar Theorem | p. 103 |
Chapter Summary | p. 116 |
Testing Your Knowledge | p. 117 |
Foundations of Geometry 2: Triangles, Quadrilaterals, Circles | p. 119 |
Overview | p. 119 |
Triangles, Congruence Relations, SAS Hypothesis | p. 120 |
Taxicab Geometry: Geometry without SAS Congruence | p. 127 |
SAS, ASA, SSS Congruence, and Perpendicular Bisectors | p. 139 |
Exterior Angle Inequality | p. 152 |
The Inequality Theorems | p. 166 |
Additional Congruence Criteria | p. 174 |
Quadrilaterals | p. 183 |
Circles | p. 194 |
Chapter Summary | p. 208 |
Testing Your Knowledge | p. 209 |
Euclidean Geometry: Trigonometry, Coordinates and Vectors | p. 211 |
Overview | p. 211 |
Euclidean Parallelism, Existence of Rectangles | p. 211 |
Parallelograms and Trapezoids: Parallel Projection | p. 224 |
Similar Triangles, Pythagorean Theorem, Trigonometry | p. 236 |
Regular Polygons and Tiling | p. 254 |
The Circle Theorems | p. 269 |
Euclid's Concept of Area and Volume | p. 284 |
Coordinate Geometry and Vectors | p. 301 |
Some Modern Geometry of the Triangle | p. 315 |
Chapter Summary | p. 328 |
Testing Your Knowledge | p. 329 |
Transformations in Geometry | p. 331 |
Overview | p. 331 |
Euclid's Superposition Proof and Plane Transformations | p. 331 |
Reflections: Building Blocks for Isometries | p. 341 |
Translations, Rotations, and Other Isometries | p. 353 |
Other Linear Transformations | p. 362 |
Coordinate Characterizations | p. 373 |
Transformation Groups | p. 389 |
Using Tranformation Theory in Proofs | p. 402 |
Chapter Summary | p. 418 |
Testing Your Knowledge | p. 419 |
Alternate Concepts for Parallelism: Non-Euclidean Geometry | p. 421 |
Overview | p. 421 |
Historical Background of Non-Euclidean Geometry | p. 421 |
An Improbable Logical Case | p. 425 |
Hyperbolic Geometry: Angle Sum Theorem | p. 436 |
Two Models for Hyperbolic Geometry | p. 445 |
Circular Inversion: Proof of SAS Postulate for Half-Plane Model | p. 469 |
Chapter Summary | p. 489 |
Testing Your Knowledge | p. 490 |
An Introduction to Three-Dimensional Geometry | p. 493 |
Overview | p. 493 |
Orthogonality Concepts for Lines and Planes | p. 493 |
Parallelism in Space: Prisms, Pyramids, and the Platonic Solids | p. 503 |
Cones, Cylinders, and Spheres | p. 514 |
Volume in E[superscript 3] | p. 522 |
Coordinates, Vectors, and Isometries in E[superscript 3] | p. 532 |
Spherical Geometry | p. 545 |
Chapter Summary | p. 559 |
Testing Your Knowledge | p. 560 |
Appendixes | |
Bibliography | p. 1 |
Review of Topics in Secondary School Geometry | p. 2 |
The Geometer's Sketchpad: Brief Instructions | p. 27 |
Unified Axiom System for the Three Classical Geometries | p. 31 |
Answers to Selected Problems | p. 35 |
Symbols, Definitions, Axioms, Theorems, and Corollaries | p. 55 |
Index | p. 1 |
Special Topics | |
An Introduction to Projective Geometry | |
An Introduction to Convexity Theory | |
Table of Contents provided by Syndetics. All Rights Reserved. |
The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.