Topics in Geometry

Topics in Geometry

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This volume presents a self-contained survey of topics in Euclidean and non-Euclidean geometry. The author's emphasis on the connections between Euclidean and non-Euclidean geometry unifies the range of topics covered. The text opens with a brief review of elementary geometry before proceeding to advanced material. Topics covered include advanced Euclidean and non-Euclidean geometry, division ratios and triangles, transformation geometry, projective geometry, conic sections, and hyperbolic and absolute geometry.
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Product details

  • Hardback | 538 pages
  • 165.1 x 231.14 x 30.48mm | 839.14g
  • Academic Press Inc
  • San Diego, United States
  • English
  • 800 illustrations, index
  • 0121027406
  • 9780121027407

Table of contents

Division Ratios and Triangles: Elementary Euclidean Geometry. Division Ratios. Menelaus' Theorem. Cava's Theorem. The Euler Line. The Nine-Point Circle and the Equicircles. Circles and Directed Distances. Transformation Geometry: Isometries. Wallpaper Groups and Translations. Axes and Centers of Wallpaper Groups. Wallpaper Groups without Rotations. Wallpaper Groups with 90o Rotations. Wallpaper Groups with only I 80o or with 120o Rotations. Dilations. Projective Geometry: The Extended Plane. Pappus' Theorem and Projections between Planes. Desargues' Theorem and Duality. Harmonic Sets. Triangles and Conic Sections. Conic Sections. Cross-Ratios. Polygons Inscribed in Conic Sections. Graphs of Quadratic Equations. Characterizations of Conic Sections. Axiomatic Geometry: Inversion in Circles. The Hyperbolic Plane. Absolute Geometry. Axiomatic Euclidean and Hyperbolic Geometry.
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