Skip to main content Accessibility help
×
  1. Home
  2. Books
  3. Non-Euclidean Geometry
  • Cited by 65
    • The digital format of this book is no longer available to purchase from Cambridge Core. Other formats may be available.
      • Show more authors
      • You may already have access via personal or institutional login
    • Select format
    • Publisher:
      Mathematical Association of America
      Publication date:
      Invalid date
      June 1998
      ISBN:
      9780883855225
      DOI:
      https://doi.org/10.5948/9781614445166
      Dimensions:
      Weight & Pages:
      Dimensions:
      Weight & Pages:
      00kg,
      • Subjects:
      Mathematics, Geometry and Topology
      Series:
      Spectrum
    You may already have access via personal or institutional login
    Selected: Digital
    Add to cart View cart Buy from Cambridge.org
    Subjects:
    Mathematics, Geometry and Topology
    Series:
    Spectrum
    Information

    Book description

    Throughout most of this book, non-Euclidean geometries in spaces of two or three dimensions are treated as specializations of real projective geometry in terms of a simple set of axioms concerning points, lines, planes, incidence, order and continuity, with no mention of the measurement of distances or angles. This synthetic development is followed by the introduction of homogeneous coordinates, beginning with Von Staudt's idea of regarding points as entities that can be added or multiplied. Tranformations that preserve incidence are called collineations. They lead in a natural way to isometries or 'congruent transformations'. Following a recommendation by Bertrand Russell, continuity is described in terms of order. Elliptic and hyperbolic geometries are derived from real projective geometry by specializing an elliptic or hyperbolic polarity which transforms points into lines (in two dimensions) or planes (in three dimensions) and vice versa.

    Refine List

    Actions for selected content:

    Select all | Deselect all
    • View selected items
    • Export citations
    • Download PDF (zip)
    • Save to Kindle
    • Save to Dropbox
    • Save to Google Drive

    Save Search

    You can save your searches here and later view and run them again in "My saved searches".

    Please provide a title, maximum of 40 characters.
    Cancel
    ×

    Contents

    Contents

    Metrics

    Full text views

    Total number of HTML views: 0
    Total number of PDF views: 0 *
    Loading metrics...

    Book summary page views

    Total views: 0 *
    Loading metrics...

    * Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

    Usage data cannot currently be displayed.

    Accessibility standard: Unknown

    Why this information is here

    This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

    Accessibility Information

    Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.