The Elements of Non-Euclidean Plane Geometry and Trigonometry

The Elements of Non-Euclidean Plane Geometry and Trigonometry
Author: Horatio Scott Carslaw
Publisher: Legare Street Press
Total Pages: 0
Release: 2022-10-27
Genre:
ISBN: 9781016470438

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

The Elements of Non-Euclidean Plane Geometry and Trigonometry - Illustrated

The Elements of Non-Euclidean Plane Geometry and Trigonometry - Illustrated
Author: H. S. Carslaw
Publisher: Merchant Books
Total Pages: 192
Release: 2007-05-01
Genre: Mathematics
ISBN: 9781603860093

An Unabridged Printing, To Include Over 100 Figures - Chapters: The Parallel Postulate, And The Work Of Saccheri, Legendre, And Gauss - The Work Of Bolyai, Lobatschewsky, And Riemann, The Founders Of Non-Euclidean Geometries - The Hyperbolic Plane Geometry - The Hyperbolic Plane Trigonometry - Measurements Of Length And Area, With The Aid Of The Infinitesimal Calculus - The Elliptic Geometry - The Elliptic Plane Trigonometry - The Consistency Of The Non-Euclidian Geometries And The Impossibility Of Proving The Parallel Postulate - Index Of Authors - Comprehensive Subject Index

Introduction to Non-Euclidean Geometry

Introduction to Non-Euclidean Geometry
Author: Harold E. Wolfe
Publisher: Courier Corporation
Total Pages: 274
Release: 2012-01-01
Genre: Mathematics
ISBN: 0486498506

One of the first college-level texts for elementary courses in non-Euclidean geometry, this volumeis geared toward students familiar with calculus. Topics include the fifth postulate, hyperbolicplane geometry and trigonometry, and elliptic plane geometry and trigonometry. Extensiveappendixes offer background information on Euclidean geometry, and numerous exercisesappear throughout the text.Reprint of the Holt, Rinehart & Winston, Inc., New York, 1945 edition

Geometry Illuminated

Geometry Illuminated
Author: Matthew Harvey
Publisher: The Mathematical Association of America
Total Pages: 561
Release: 2015-09-25
Genre: Mathematics
ISBN: 1939512115

Geometry Illuminated is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very "visual" subject. This book hopes to takes full advantage of that, with an extensive use of illustrations as guides. Geometry Illuminated is divided into four principal parts. Part 1 develops neutral geometry in the style of Hilbert, including a discussion of the construction of measure in that system, ultimately building up to the Saccheri-Legendre Theorem. Part 2 provides a glimpse of classical Euclidean geometry, with an emphasis on concurrence results, such as the nine-point circle. Part 3 studies transformations of the Euclidean plane, beginning with isometries and ending with inversion, with applications and a discussion of area in between. Part 4 is dedicated to the development of the Poincaré disk model, and the study of geometry within that model. While this material is traditional, Geometry Illuminated does bring together topics that are generally not found in a book at this level. Most notably, it explicitly computes parametric equations for the pseudosphere and its geodesics. It focuses less on the nature of axiomatic systems for geometry, but emphasizes rather the logical development of geometry within such a system. It also includes sections dealing with trilinear and barycentric coordinates, theorems that can be proved using inversion, and Euclidean and hyperbolic tilings.

Euclid's Elements

Euclid's Elements
Author: Euclid
Publisher:
Total Pages: 544
Release: 2002
Genre: Mathematics
ISBN:

"The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary" --from book jacket.

Geometry with an Introduction to Cosmic Topology

Geometry with an Introduction to Cosmic Topology
Author: Michael P. Hitchman
Publisher: Jones & Bartlett Learning
Total Pages: 255
Release: 2009
Genre: Mathematics
ISBN: 0763754579

The content of Geometry with an Introduction to Cosmic Topology is motivated by questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have and edge? Is it infinitely big? Dr. Hitchman aims to clarify this fascinating area of mathematics. This non-Euclidean geometry text is organized intothree natural parts. Chapter 1 provides an overview including a brief history of Geometry, Surfaces, and reasons to study Non-Euclidean Geometry. Chapters 2-7 contain the core mathematical content of the text, following the ErlangenProgram, which develops geometry in terms of a space and a group of transformations on that space. Finally chapters 1 and 8 introduce (chapter 1) and explore (chapter 8) the topic of cosmic topology through the geometry learned in the preceding chapters.

The Foundations of Geometry

The Foundations of Geometry
Author: David Hilbert
Publisher: Read Books Ltd
Total Pages: 139
Release: 2015-05-06
Genre: History
ISBN: 1473395941

This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.