Thinking geometrically : a survey of geometries

書誌事項

Thinking geometrically : a survey of geometries

Thomas Q. Sibley

(MAA textbooks)

Mathematical Association of America, c2015

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注記

Includes index

内容説明・目次

内容説明

This is a self-contained, comprehensive survey of college geometry that can serve a wide variety of courses for students of both mathematics and mathematics education. The text develops visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. Chapter topics include Euclidean geometry, axiomatic systems and models, analytic geometry, transformational geometry, symmetry, non-Euclidean geometry, projective geometry, finite geometry, differential geometry, and discrete geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics. Appendices include material from Euclid's first book, as well as Hilbert's axioms, and provide brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters.

目次

  • Preface
  • 1. Euclidean geometry
  • 2. Axiomatic systems
  • 3. Analytic geometry
  • 4. Non-Euclidean geometries
  • 5. Transformational geometry
  • 6. Symmetry
  • 7. Projective geometry
  • 8. Finite geometries
  • 9. Differential geometry
  • 10. Discrete geometry
  • 11. Epilogue
  • Appendix A. Definitions, postulates, common notions, and propositions from Book I of Euclid's Elements
  • Appendix B. SMSG axioms for Euclidean geometry
  • Appendix C. Hilbert's axioms for Euclidean plane geometry
  • Appendix D. Linear algebra summary
  • Appendix E. Multivariable calculus summary
  • Appendix F. Elements of proofs
  • Answers to selected exercises
  • Acknowledgements
  • Index.

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詳細情報

  • NII書誌ID(NCID)
    BB2165978X
  • ISBN
    • 9781939512086
  • LCCN
    2015936100
  • 出版国コード
    us
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    [Washington, DC]
  • ページ数/冊数
    xxiii, 559 p.
  • 大きさ
    27 cm
  • 分類
  • 件名
  • 親書誌ID
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