This text presents geometry in an exemplary, accessible and attractive form. The book emphasizes both the intellectually stimulating parts of geometry and routine arguments or computations in concrete or classical cases, as well as practical and physical applications. The book also teaches the student fundamental concepts and the difference between important reults and minor technical routines. Altogether, the text presents a coherent high school curriculum for the geometry course. There are many examples and exercises.
Author(s): Serge Lang, Gene Murrow
Edition: 2nd
Publisher: Springer
Year: 1988
Language: English
Pages: 408
Contents......Page 6
Introduction......Page 10
§1. Lines......Page 14
§2. Distance......Page 21
§3. Angles......Page 26
§4. Proofs......Page 42
§5. Right Angles and Perpendicularity......Page 49
§6. The Angles of a Triangle......Page 59
§7. An Application: Angles of Reflection......Page 75
§1. Coordinate Systems......Page 78
§2. Distance Between Points on a Line......Page 84
§3. Equation of a Line......Page 86
§1. The Area of a Triangle......Page 94
§2. The Pythagoras Theorem......Page 108
§1. Distance Between Arbitrary Points......Page 123
§2. Higher Dimensional Space......Page 127
§3. Equation of a Circle......Page 132
CHAPTER 5 Some Applications of Right Triangles......Page 136
§1. Perpendicular Bisector......Page 137
§2. Isosceles and Equilateral Triangles......Page 149
§3. Theorems About Circles......Page 161
§1. Basic Ideas......Page 175
§2. Convexity and Angles......Page 178
§3. Regular Polygons......Page 182
§1. Euclid's Tests for Congruence......Page 190
§2. Some Applications of Congruent Triangles......Page 205
§3. Special Triangles......Page 213
§1. Definition......Page 223
§2. Change of Area Under Dilation......Page 231
§3. Change of Length Under Dilation......Page 245
§4. The Circumference of a Circle......Page 248
§5. Similar Triangles......Page 258
§1. Boxes and Cylinders......Page 274
§2. Change of Volume Under Dilations......Page 283
§3. Cones and Pyramids......Page 287
§4. The Volume of the Ball......Page 294
§5. The Area of the Sphere......Page 303
CHAPTER 10 Vectors and Dot Product......Page 308
§1. Vector Addition......Page 309
§2. The Scalar Product......Page 314
§3. Perpendicularity......Page 317
§4. Projections......Page 322
§5. Ordinary Equation for a Line......Page 325
§6. The 3-Dimensional Case......Page 329
§7. Equation for a Plane in 3-Space......Page 332
§1. Introduction......Page 334
§2. Symmetry and Reflections......Page 337
§3. Terminology......Page 344
§4. Reflection Through a Line......Page 345
§5. Reflection Through a Point......Page 350
§6. Rotations......Page 353
§7. Translations......Page 359
§8. Translations and Coordinates......Page 361
§1. Definitions and Basic Properties......Page 369
§2. Relations with Coordinates......Page 376
§3. Composition of Isometries......Page 380
§4. Definition of Congruence......Page 390
§5. Proofs of Euclid's Tests for Congruent Triangles......Page 394
§6. Isometries as Compositions of Reflections......Page 397
Index......Page 404
