Skip to content
Register Sign in Wishlist

Geometries and Transformations

  • Date Published: June 2018
  • availability: In stock
  • format: Hardback
  • isbn: 9781107103405

Hardback

Add to wishlist

Other available formats:
eBook


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • Euclidean and other geometries are distinguished by the transformations that preserve their essential properties. Using linear algebra and transformation groups, this book provides a readable exposition of how these classical geometries are both differentiated and connected. Following Cayley and Klein, the book builds on projective and inversive geometry to construct 'linear' and 'circular' geometries, including classical real metric spaces like Euclidean, hyperbolic, elliptic, and spherical, as well as their unitary counterparts. The first part of the book deals with the foundations and general properties of the various kinds of geometries. The latter part studies discrete-geometric structures and their symmetries in various spaces. Written for graduate students, the book includes numerous exercises and covers both classical results and new research in the field. An understanding of analytic geometry, linear algebra, and elementary group theory is assumed.

    • Provides a unified framework for describing Euclidean and non-Euclidean geometries
    • Demonstrates the interconnectedness of different geometries using linear algebra
    • Includes both classical results and contemporary research, as well as numerous exercises
    Read more

    Reviews & endorsements

    'This extremely valuable book tells the story about classical geometries - euclidean, spherical, hyperbolic, elliptic, unitary, affine, projective - and how they all fit together. At the center are geometric transformation groups, both continuous groups such as isometry or collineation groups, and their discrete subgroups occurring as symmetry groups of polytopes, tessellations, or patterns, including reflection groups. I highly recommend the book!' Egon Schulte, Northeastern University, Massachusetts

    'This is a book written with a passion for geometry, for complete lists, for consistent notation, for telling the history of a concept, and a passion to give an insight into a situation before going into the details.' Erich W. Ellers, zbMATH

    See more reviews

    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: June 2018
    • format: Hardback
    • isbn: 9781107103405
    • length: 452 pages
    • dimensions: 241 x 162 x 27 mm
    • weight: 0.81kg
    • availability: In stock
  • Table of Contents

    Introduction
    1. Homogenous spaces
    2. Linear geometries
    3. Circular geometries
    4. Real collineation groups
    5. Equiareal collineations
    6. Real isometry groups
    7. Complex spaces
    8. Complex collineation groups
    9. Circularities and concatenations
    10. Unitary isometry groups
    11. Finite symmetry groups
    12. Euclidean symmetry groups
    13. Hyperbolic coxeter groups
    14. Modular transformations
    15. Quaternionic modular groups.

  • Author

    Norman W. Johnson, Wheaton College, Massachusetts
    Norman W. Johnson was Professor Emeritus of Mathematics at Wheaton College, Massachusetts. Johnson authored and co-authored numerous journal articles on geometry and algebra, and his 1966 paper 'Convex Polyhedra with Regular Faces' enumerated what have come to be called the Johnson solids. He was a frequent participant in international conferences and a member of the American Mathematical Society and the Mathematical Association of America.

Related Books

Sorry, this resource is locked

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

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 www.ebooks.com. Please see the permission section of the www.ebooks.com 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.

Cancel

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.
×