Non-Euclidean Geometry

$13.95

Publication Date: 8th June 2012

This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.
Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geomet... Read More
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This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.
Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geomet... Read More
Description
This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.
Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of sufficiently small domains, spherical and analytical geometry, the Klein model, and other topics. Appendixes include a table of values of hyperbolic functions.

Reprint of the Pergamon Press, Inc., New York, 1961 edition.
Details
  • Price: $13.95
  • Pages: 208
  • Publisher: Dover Publications
  • Imprint: Dover Publications
  • Series: Dover Books on Mathematics
  • Publication Date: 8th June 2012
  • Trim Size: 5.37 x 8.5 in
  • ISBN: 9780486155012
  • Format: eBook
  • BISACs:
    MATHEMATICS / Geometry / Non-Euclidean
Author Bio
The author was a Professor at the University of Warsaw.
Table of Contents
Preface
I. From the history of geometry
II. The principles of non-Euclidean geometry
III. Further development of the theory
Appendices
Table of values of hyperbolic functions
Index
This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.
Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of sufficiently small domains, spherical and analytical geometry, the Klein model, and other topics. Appendixes include a table of values of hyperbolic functions.

Reprint of the Pergamon Press, Inc., New York, 1961 edition.
  • Price: $13.95
  • Pages: 208
  • Publisher: Dover Publications
  • Imprint: Dover Publications
  • Series: Dover Books on Mathematics
  • Publication Date: 8th June 2012
  • Trim Size: 5.37 x 8.5 in
  • ISBN: 9780486155012
  • Format: eBook
  • BISACs:
    MATHEMATICS / Geometry / Non-Euclidean
The author was a Professor at the University of Warsaw.
Preface
I. From the history of geometry
II. The principles of non-Euclidean geometry
III. Further development of the theory
Appendices
Table of values of hyperbolic functions
Index