A course in modern geometries


A course in modern geometries

Judith N. Cederberg

(Undergraduate texts in mathematics)

Springer, c2001

2nd ed

大学図書館所蔵 件 / 37



Includes bibliographical references (p. 413-425) and index



Designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. The first chapter presents several finite geometries in an axiomatic framework, while Chapter 2 continues the synthetic approach in introducing both Euclids and ideas of non-Euclidean geometry. There follows a new introduction to symmetry and hands-on explorations of isometries that precedes an extensive analytic treatment of similarities and affinities. Chapter 4 presents plane projective geometry both synthetically and analytically, and the new Chapter 5 uses a descriptive and exploratory approach to introduce chaos theory and fractal geometry, stressing the self-similarity of fractals and their generation by transformations from Chapter 3. Throughout, each chapter includes a list of suggested resources for applications or related topics in areas such as art and history, plus this second edition points to Web locations of author-developed guides for dynamic software explorations of the Poincare model, isometries, projectivities, conics and fractals. Parallel versions are available for "Cabri Geometry" and "Geometers Sketchpad".


1 Axiomatic Systems and Finite Geometries.- 2 Non-Euclidean Geometry.- 3 Geometric Transformations of the Euclidean Plane.- 4 Projective Geometry.- 5 Chaos to Symmetry: An Introduction to Fractal Geometry.- Appendices.- B Hilbert's Axioms for Plane Geometry.- C Birkhoff's Postulates for Euclidean Plane Geometry.- D The SMSG Postulates for Euclidean Geometry.- E Some SMSG Definitions for Euclidean Geometry.- F The ASA Theorem.- References.

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  • ISBN
    • 0387989722
  • LCCN
  • 出版国コード
  • タイトル言語コード
  • 本文言語コード
  • 出版地
    New York
  • ページ数/冊数
    xix, 442 p.
  • 大きさ
    25 cm
  • 分類
  • 件名
  • 親書誌ID