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Geometric Transformations

Geometric Transformations

Volume 4. Circular Transformations

£34.99

Part of Anneli Lax New Mathematical Library

  • Date Published: October 2009
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • format: Paperback
  • isbn: 9780883856482

£ 34.99
Paperback

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  • The familiar plane geometry of secondary school - figures composed of lines and circles - takes on a new life when viewed as the study of properties that are preserved by special groups of transformations. No longer is there a single, universal geometry: different sets of transformations of the plane correspond to intriguing, disparate geometries. This book is the concluding Part IV of Geometric Transformations, but it can be studied independently of Parts I, II, and III. The present Part IV develops the geometry of transformations of the plane that map circles to circles (conformal or anallagmatic geometry). The notion of inversion, or reflection in a circle, is the key tool employed. Applications include ruler-and-compass constructions and the Poincaré model of hyperbolic geometry. The straightforward, direct presentation assumes only some background in elementary geometry and trigonometry.

    • Numerous exercises lead the reader to a mastery of the methods and concepts
    • The second half of the book contains detailed solutions of all the problems
    • Accessible to undergraduates - assumes only familiarity with elementary geometry and trigonometry
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    Product details

    • Date Published: October 2009
    • format: Paperback
    • isbn: 9780883856482
    • length: 293 pages
    • dimensions: 229 x 153 x 15 mm
    • weight: 0.4kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • Table of Contents

    1. Reflection in a circle (inversion)
    Notes to Section 1
    2. Application of inversions to the solution of construction
    Problems: constructions with compass alone
    Problems involving the construction of circles
    Notes to Section 2
    3. Pencils of circles. The radical axis of two circles
    Notes to Section 3
    4. Inversion (concluding section)
    Notes to Section 4
    5. Axial circular transformations
    A. Dilatation
    B. Axial inversion
    Notes to Section 5
    Supplement I
    Non-euclidean geometry of Lobachevskii-Bolyai, or hyperbolic geometry
    Notes to Supplement I
    Solutions
    Section 1
    Section 2
    Section 3
    Circular transformations
    Section 4
    Section 5
    Supplement II
    Notes to Supplement II.

  • Author

    I. M. Yaglom
    I. M. Yaglom authored many books which have since become academic standards of reference. These include Complex Numbers in Geometry, Geometric Transformations, A Simple Non-Euclidean Geometry and its Physical Basis, and Probability and Information. He was Professor of Mathematics at Yaroslavl State University from 1974–83 and a technical consultant at the Academy of Pedagogical Sciences from 1984–88.

    Translator

    Abe Shenitzer
    Abe Shenitzer has translated many mathematics classics (from German, Polish and Russian into English). He retired in 1989 from York University, where he had been Professor of Mathematics since 1969.

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