5 edition of **Euclidean and non-Euclidean geometries** found in the catalog.

Euclidean and non-Euclidean geometries

Marvin J. Greenberg

- 77 Want to read
- 14 Currently reading

Published
**2008**
by W.H. Freeman in New York
.

Written in English

- Geometry.,
- Geometry, Non-Euclidean.,
- Geometry -- History.,
- Geometry, Non-Euclidean -- History.

**Edition Notes**

Includes bibliographical references (p. 603-610) and indexes.

Statement | Marvin Jay Greenberg. |

Classifications | |
---|---|

LC Classifications | QA445 .G84 2008 |

The Physical Object | |

Pagination | xxix, 637 p. : |

Number of Pages | 637 |

ID Numbers | |

Open Library | OL21812051M |

ISBN 10 | 0716799480 |

ISBN 10 | 9780716799481 |

LC Control Number | 2007928758 |

Thanks for A2A, George. However first read a disclaimer: I've never been comfortable with Euclidean geometry, and, actually, I had even dislike for this sort of math. So my geometric knowledge is fairly limited and lacking coherency. Moreove. as an introduction to spherical, locally euclidean, and a little hyperbolic geometry i like very much the book Geometries and Groups by Shafarevich and Nikulin. another excellent book is stillwell's geometry of surfaces, and if you want the original book on non euclidean geometry you can take a look at euclides vindicatus by saccheri.

Non-Euclidean Geometry: non-Euclidean geometry is any geometry that is different from Euclidean geometry. Each Non-Euclidean geometry is a consistent system of definitions, assumptions, and proofs that describe such objects as points, lines and planes. The two most common non-Euclidean geometries are spherical geometry and hyperbolic geometry. Euclidean And Non-Euclidean Geometry: Development and History, Hardcover by Greenberg, Marvin Jay, ISBN , ISBN , Brand New, Free shipping in the US This is the definitive presentation of the history, development and philosophical significance of non-Euclidean geometry as well as of the rigorous foundations for it and /5(77).

Euclidean geometry only deals with straight lines, while non-Euclidean geometry is the study of triangles. Euclidean geometry assumes that the surface is flat, while non-Euclidean geometry studies. Euclid developed a set of postulates and essentially created what most of us call geometry. All of the rules that you think of as governing how we measure things in 2D and 3D are proved from these postulates (usually in a bit of a cleaned up versi.

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A reissue of Professor Coxeter's classic text on non-Euclidean geometry. It surveys real projective geometry, and elliptic geometry.

After this the Euclidean and hyperbolic geometries are built up Euclidean and non-Euclidean geometries book as special cases. This is essential reading for anybody with Euclidean and non-Euclidean geometries book interest in by: 1.

This book surveys these geometries, including non-Euclidean metric geometries (hyperbolic geometry and elliptic geometry) and nonmetric geometries (for example, projective geometry), The study of such geometries complements and deepens the knowledge of the world contained in Euclidean geometry.

Modern geometry is a fascinating and important /5(2). euclidean and non euclidean geometry Download euclidean and non euclidean geometry or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get euclidean and non euclidean geometry book now.

This site is like a library, Use search box in the widget to get ebook that you want. Euclidean & Non-Euclidean Geometries book. Read 9 reviews from the world's largest community for readers. This classic text provides overview of both cla /5.

: Euclidean and Non-Euclidean Geometries: Development and History () by Greenberg, Marvin J. and a great selection of similar New, /5(77).

This is the fourth edition of a particularly fine text by Marvin Jay Greenberg. If you want to learn about Euclidean and non-Euclidean geometriesthe great contributions of Bolyai and Lobachevskythis is the place to do it. The book is authoritative but warm and inviting.

It is full of good history and full of good mathematics.5/5(5). Non-Euclidean Geometry first examines the various attempts to prove Euclid's parallel postulate-by the Greeks, Arabs, and mathematicians of the Renaissance.

Then, ranging through the 17th, 18th and 19th centuries, it considers the forerunners and founders of non-Euclidean geometry, such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss.

Euclidean and Non-Euclidean Geometries. Development and History Marvin Jay Greenberg. This classic text provides overview of both classic and hyperbolic geometries, placing the work of key mathematicians/ philosophers in historical context.

You can write a book review and share your experiences. Other readers will always be interested in. Non-Euclidean geometries. New York, NY: Springer, This is a collective volume published in the memory of Janos Bolyai. It contains contributions of great variety, both in approach and difficulty.

Trudeau, Richerd J. The non-Euclidean revolution. Boston, MA: Birkhauser, Perhaps the most quoted book on non-Euclidean geometry. Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the 's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from gh many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show.

The MAA is delighted to be the publisher of the sixth edition of this book, updated with a new section on the author's useful concept of inversive distance.

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.

Beltrami's work on a model of Bolyai - Lobachevsky's non-Euclidean geometry was completed by Klein in Klein went further than this and gave models of other non-Euclidean geometries such as Riemann's spherical geometry.

Klein's work was based on a notion of distance defined by Cayley in when he proposed a generalised definition for. In this book the author has attempted to treat the Elements of Non-Euclidean Plane Geometry and Trigonometry in such a way as to prove useful to teachers of Elementary Geometry in schools and colleges.

Hyperbolic and elliptic geometry are covered. ( views) The Elements of Non-Euclidean Geometry by D.M.Y. Sommerville - & Sons Ltd., His Freeman text Euclidean and Non-Euclidean Geometries: Development and History had its first edition appear inand is now in its vastly expanded fourth edition.

His early journal publications are in the subject of algebraic geometry, where he discovered a functor J.-P. Serre named after him and an approximation theorem J. Nicaise and J. The non-Euclidean geometries developed along two different historical threads.

The first thread started with the search to understand the movement of stars and planets in the apparently hemispherical sky. For example, Euclid (flourished c. bc) wrote about spherical geometry in his astronomical work Phaenomena.

In addition to looking to the. This book is an attempt to give a simple and direct account of the Non-Euclidean Geometry, and one which presupposes but little knowledge of Math-ematics. The ﬁrst three chapters assume a knowledge of only Plane and Solid Geometry and Trigonometry, and the entire book can be read by one who has.

The discoverers of non-Euclidean geometries were four mathematics geniuses named Lobachevsky, Bolyai, Gauss, and Riemann. Nikolai Lobachevsky (–) was teaching at Kazan University, in Russia, when he published his results on an “imaginary geometry” (which would later be called hyperbolic), in Disk Models of non-Euclidean Geometry Beltrami and Klein made a model of non-Euclidean geometry in a disk, with chords being the lines.

But angles are measured in a complicated way. Poincaré discovered a model made from points in a disk and arcs of circles orthogonal to the boundary of the disk.

Angles are measured in the usual Size: KB. A modern approach based on the systematic use of transformations—Uses the complex plane and geometric transformations to present a wide variety of geometries.

Reflects a major theme in modern geometry. Ex.___ Coverage of a great variety of geometries—Both non-Euclidean and nonmetric—e.g., Möbius geometry, hyperbolic plane geometry, elliptic plane geometry, absolute geometry, and Availability: Available.

first introduced the author to non-Euclidean geometries, and to Jean-Marie Laborde for his permission to include the demonstration version of his software, Cabri II, with this thesis. Thanks also to Euclid, Henri Poincaré, Felix Klein, Janos Bolyai, and all other pioneers in the field of geometry.

Euclidean and non-Euclidean geometries: development and history Marvin J Greenberg This is the definitive presentation of the history, development and philosophical significance of non-Euclidean geometry as well as of the rigorous foundations for it and for elementary Euclidean geometry, essentially according to Hilbert.

Eugenio Beltrami ( – ) showed for the first time that non-Euclidean geometries could have a model. Inin his essay Essay on the interpretation of non-euclidean geometry, Beltrami introduced a model for non-Euclidean geometry in 3-dimensional Euclidean geometry.One of the first college-level texts for elementary courses in non-Euclidean geometry, this volume is geared toward students familiar with calculus.

Topics include the fifth postulate, hyperbolic plane geometry and trigonometry, and elliptic plane geometry and trigonometry. Extensive appendixes offer background information, and numerous exercises appear throughout the text.

edition.