Elementary Euclidean geometry : an introduction

C.G. Gibson

This book, first published in 2004, is a genuine introduction to the geometry of lines and conics in the Euclidean plane. Lines and circles provide the starting point, with the classical invariants of general conics introduced at an early stage, yielding a broad subdivision into types, a prelude to the congruence classification. A recurring theme is the way in which lines intersect conics. From single lines one proceeds to parallel pencils, leading to midpoint loci, axes and asymptotic directions. Likewise, intersections with general pencils of lines lead to the central concepts of tangent, normal, pole and polar. The treatment is example based and self contained, assuming only a basic grounding in linear algebra. With numerous illustrations and several hundred worked examples and exercises, this book is ideal for use with undergraduate courses in mathematics, or for postgraduates in the engineering and physical sciences.

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[目次]

  • 1. Points and lines
  • 2. The Euclidean plane
  • 3. Circles
  • 4. General conics
  • 5. Centres of general conics
  • 6. Degenerate conics
  • 7. Axes and asymptotes
  • 8. Focus and directrix
  • 9. Tangents and normals
  • 10. The parabola
  • 11. The ellipse
  • 12. The hyperbola
  • 13. Pole and polar
  • 14. Congruences
  • 15. Classifying conics
  • 16. Distinguishing conics
  • 17. Uniqueness and invariance.

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この本の情報

書名 Elementary Euclidean geometry : an introduction
著作者等 Gibson, Christopher G.
Gibson C. G.
書名別名 Elementary Euclidean geometry : an undergraduate introduction
出版元 Cambridge University Press
刊行年月 2003
ページ数 xvi, 174 p.
大きさ 24 cm
ISBN 0521834481
NCID BA67171499
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言語 英語
出版国 イギリス
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