Skip to content
Register Sign in Wishlist
Geometric Transformations

Geometric Transformations

Volume 4. Circular Transformations


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

This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
Unavailable Add to wishlist

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • 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
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    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
    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.


    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.

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.