Topics in Geometry / Edition 1

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Editorial Reviews

Booknews
A text for a junior-level college geometry course for prospective secondary school teachers and other math majors with only calculus as a prerequisite. A diversity of topics are considered in the areas of division ratios and triangles, transformational geometry, projective geometry, conic sections, and axiomatic geometry. Emphasis is placed on the connections between Euclidean and non-Euclidean geometry. Exercises are provided. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780121027407
  • Publisher: Elsevier Science & Technology Books
  • Publication date: 2/28/1994
  • Edition number: 1
  • Pages: 538

Table of Contents

Preface
Ch. I Division Ratios and Triangles 1
Sect. 0 Elementary Euclidean Geometry 4
Sect. 1 Division Ratios 21
Sect. 2 Menelaus' Theorem 42
Sect. 3 Ceva's Theorem 56
Sect. 4 The Euler Line 74
Sect. 5 The Nine-Point Circle and the Equicircles 91
Sect. 6 Circles and Directed Distances 110
Ch. II Transformation Geometry 133
Sect. 7 Isometries 135
Sect. 8 Wallpaper Groups and Translations 153
Sect. 9 Axes and Centers of Wallpaper Groups 172
Sect. 10 Wallpaper Groups without Rotations 189
Sect. 11 Wallpaper Groups with 90[degree] Rotations 204
Sect. 12 Wallpaper Groups with only 180[degree] or with 120[degree] Rotations 224
Sect. 13 Dilations 246
Ch. III Projective Geometry 263
Sect. 14 The Extended Plane 266
Sect. 15 Pappus' Theorem and Projections Between Planes 282
Sect. 16 Desargues' Theorem and Duality 306
Sect. 17 Harmonic Sets 326
Sect. 18 Triangles and Conic Sections 344
Ch. IV Conic Sections 367
Sect. 19 Cross-Ratios 369
Sect. 20 Polygons Inscribed in Conic Sections 390
Sect. 21 Graphs of Quadratic Equations 412
Sect. 22 Characterizations of Conic Sections 431
Ch. V Axiomatic Geometry 449
Sect. 23 Inversion in Circles 452
Sect. 24 The Hyperbolic Plane 473
Sect. 25 Absolute Geometry 493
Sect. 26 Axiomatic Euclidean and Hyperbolic Geometry 511
Index 533
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