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Thinking Geometrically

Thinking Geometrically
A Survey of Geometries


Part of Mathematical Association of America Textbooks

  • Date Published: December 2015
  • availability: Temporarily unavailable - available from TBC
  • format: Hardback
  • isbn: 9781939512086

£ 45.00

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About the Authors
  • 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.

    • Emphasises the best aspects of geometrical thinking: its beauty, visual insights, convincing proofs, broad connections, and more
    • The book's focus on developing reason and intuition will appeal to both students of mathematics and mathematics education
    • Historical material and biographies of famous geometers share some of the rich insights that history can provide
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    Product details

    • Date Published: December 2015
    • format: Hardback
    • isbn: 9781939512086
    • length: 509 pages
    • dimensions: 262 x 182 x 35 mm
    • weight: 1.13kg
    • availability: Temporarily unavailable - available from TBC
  • Table of Contents

    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

  • Author

    Thomas Q. Sibley, Saint John's University, Minnesota
    Thomas Q. Sibley is a Professor of Mathematics at Saint John's University, Minnesota. He has taught mathematics in the Democratic Republic of the Congo and Liberia as well as in the USA, and has received several teaching awards, including the Distinguished Teaching Award from the MAA, North Central Section (2003). He is a member of the American Mathematical Society, the Association for Women in Mathematics, the Society for Mathematical Biology, and the Council for Undergraduate Research.

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