rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Euclidean Geometry and its Subgeometries
  name:
    name part: Specht, Edward John.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Jones, Harold Trainer.
    role:
      role term: author.
  name:
    name part: Calkins, Keith G.
    role:
      role term: author.
  name:
    name part: Rhoads, Donald H.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2015
    edition: 1st ed. 2015.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIX, 527 p. 59 illus. online resource.
  abstract: In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of these, including all that are needed for this development, are available online at the homepage for the book at www.springer.com. Supplementary material is available online covering construction of complex numbers, arc length, the circular functions, angle measure, and the polygonal form of the Jordan Curve theorem. Euclidean Geometry and Its Subgeometries is intended for advanced students and mature mathematicians, but the proofs are thoroughly worked out to make it accessible to undergraduate students as well. It can be regarded as a completion, updating, and expansion of Hilbert's work, filling a gap in the existing literature.
  table of contents: Preface -- Preliminaries and Incidence Geometry (I) -- Affine Geometry: Incidence with Parallelism (IP) -- Collineations of an Affine Plane (CAP) -- Incidence and Betweenness (IB) -- Pasch Geometry (PSH) -- Ordering a Line in the Pasch Plane (ORD) -- Collineations Preserving Betweenness (COBE) -- Neutral Geometry (NEUT) -- Free Segments of a Neutral Plane (FSEG) -- Rotations about a Point of a Neutral Plane (ROT) -- Euclidean Geometry Basics (EUC) -- Isometries of a Euclidean Plane (ISM) -- Dilations of a Euclidean Plane (DLN) -- Every Line in a Euclidean Plane is an Ordered Field (OF) -- Similarity on a Euclidean Plane (SIM) -- Axial Affinities of a Euclidean Plane (AX) -- Rational Points on a Line (QX).- A Line as Real Numbers (REAL); Coordinatization of a Plane (RR) -- Belineations on a Euclidean/LUB Plane (AA) -- Ratios of Sensed Segments (RS) -- Consistency and Independence of Axioms; Other Matters Involving Models -- References -- Index.
  note: by Edward John Specht, Harold Trainer Jones, Keith G. Calkins, Donald H. Rhoads.
  subject:
    topic: Mathematics
  subject:
    topic: Geometry
  subject:
    topic: History
  subject:
    topic: Mathematics
  subject:
    topic: Geometry
  subject:
    topic: History of Mathematical Sciences
  classification: QA440-699
  classification: 516
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319237756
  identifier: http://dx.doi.org/10.1007/978-3-319-23775-6
  record info:
    record creation date: 151230
    record change date: 20151230224654.0
    record identifier: 978-3-319-23775-6