The Non-Euclidean, Hyperbolic Plane

P. Kelly

ISBN 10: 0387905529 / ISBN 13: 9780387905525

Published by Springer, Humana Jun 1981, 1981

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 348 pp. Englisch.

Seller Inventory # 9780387905525

Bibliographic Details

• Title: The Non-Euclidean, Hyperbolic Plane
• Publisher: Springer, Humana Jun 1981
• Publication Date: 1981
• Language: English
• ISBN 10: 0387905529
• ISBN 13: 9780387905525
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 19D millimeters 235 millimeters width by 155 millimeters height by 19 millimeters depth
• Weight: 528 grams
• Signed: Signed by Author(s)

About this title

Synopsis

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.