عنوان
پدید آورنده
موضوع
رده
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9780387905525
(Number (ISBN
9781461381259
NATIONAL BIBLIOGRAPHY NUMBER
Number
dltt
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
The Non-Euclidean, Hyperbolic Plane
General Material Designation
[Book]
Other Title Information
Its Structure and Consistency /
First Statement of Responsibility
by Paul Kelly, Gordon Matthews.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
New York, NY :
Name of Publisher, Distributor, etc.
Springer New York,
Date of Publication, Distribution, etc.
1981.
SERIES
Series Title
Universitext,
ISSN of Series
0172-5939
CONTENTS NOTE
Text of Note
I Some Historical Background -- 1. The Parallel-Postulate Problem -- 2. The Lost Centuries -- 3. Saccheri and the 'Near Miss' -- 4. The Correct Perspective-Gauss, Bolyai, Lobatchevsky -- 5. Not-Euclidean Geometry, Absolute Geometry -- II Absolute Plane Geometry -- 1. Linear Sets and Linear Order -- 2. Half-Planes, Angles, and Angle Measure -- 3. Triangle Relations, Congruence, Foot in a Set -- 4. Non-intersecting Lines -- 5. Dedekind Cut, Continuity, A Basic Circle Property -- 6. Motions and Symmetries -- III Hyperbolic Plane Geometry -- 1. Hyperbolic Parallels -- 2. Biangles, Hyperparallels -- 3. Saccheri and Lambert Quadrilaterals, Polygon Angle Sums -- 4. Angle of Parallelism Function, Triangle Defect, Distance Variations -- 5. The 3-Point Property, Cycles -- 6. Hyperbolic Compass and Straight Edge Constructions -- 7. Existence Problems; the Method of Associated Right Triangles -- IV A Euclidean Model of the Hyperbolic Plane -- 1. An Overview of the Model -- 2. Circular Inversions in E2 -- 3. Angle and Cross Ratio Invariance Under Inversion -- 4. Linear Order and Motions in the Model -- 5. Half-Planes, Angles and Angle Measure in the Model -- 6. Triangle Congruence in the Model, the Consistency of Hyperbolic Geometry -- Appendix Distance Geometrics -- Topic I. Metric Space and Metric Geometry -- Topic II. A Spherical Metric -- Topic III. Elliptic Geometry -- Topic IV. Barbilian Geometries, the Cross Ratio Metric.
0
SUMMARY OR ABSTRACT
Text of Note
The discovery of hyperbolic geometry, and the subsequent proof that this geometry is just as logical as Euclid's, had a profound in fluence on man's understanding of mathematics and the relation of mathematical geometry to the physical world. It is now possible, due in large part to axioms devised by George Birkhoff, to give an accurate, elementary development of hyperbolic plane geometry. Also, using the Poincare model and inversive geometry, the equiconsistency of hyperbolic plane geometry and euclidean plane geometry can be proved without the use of any advanced mathematics. These two facts provided both the motivation and the two central themes of the present work. Basic hyperbolic plane geometry, and the proof of its equal footing with euclidean plane geometry, is presented here in terms acces sible to anyone with a good background in high school mathematics. The development, however, is especially directed to college students who may become secondary teachers. For that reason, the treatment is de signed to emphasize those aspects of hyperbolic plane geometry which contribute to the skills, knowledge, and insights needed to teach eucli dean geometry with some mastery.
OTHER EDITION IN ANOTHER MEDIUM
International Standard Book Number
9780387905525
PIECE
Title
Springer eBooks
TOPICAL NAME USED AS SUBJECT
Geometry.
Mathematics.
PERSONAL NAME - PRIMARY RESPONSIBILITY
Kelly, Paul.
PERSONAL NAME - ALTERNATIVE RESPONSIBILITY
Matthews, Gordon.
CORPORATE BODY NAME - ALTERNATIVE RESPONSIBILITY
SpringerLink (Online service)
ORIGINATING SOURCE
Date of Transaction
20190307160300.0
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
