Roads to Geometry
2nd Edition
Published on 3. November 1997
Book
Hardback
447 pages
978-0-13-181652-7 (ISBN)
Description
Appropriate for junior level college geometry courses. Assumes only a prior course in high school geometry and the mathematical maturity usually provided by a semester of calculus or discrete mathematics.
This book provides a geometrical experience that unifies a mostly Euclidean approach with various non-Euclidean views of the world. It offers the reader a "map" for a voyage through plane geometry and its various branches, as well as side-trips that discuss analytic and transformational geometry.
This book provides a geometrical experience that unifies a mostly Euclidean approach with various non-Euclidean views of the world. It offers the reader a "map" for a voyage through plane geometry and its various branches, as well as side-trips that discuss analytic and transformational geometry.
More details
Edition
2nd edition
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
Professional and scholarly
Dimensions
Height: 235 mm
Width: 160 mm
Thickness: 21 mm
Weight
715 gr
ISBN-13
978-0-13-181652-7 (9780131816527)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Edward C. Wallace | Stephen F. West
Roads to Geometry
Book
08/2003
3rd Edition
Pearson
€118.72
Article exhausted; check for reprint
Previous edition
Edward C. Wallace
Roads to Geometry
Book
10/1991
Prentice-Hall
€94.03
Article exhausted; check different version
Content
1. Rules of the Road (Axiomatic Systems).
Historical Background: Axiomatic Systems and their Properties. Finite Geometries. Axioms for Incidence Geometry.
2. Many Ways to Go.
Introduction. Euclid's Geometry and Euclid's Elements. An Introduction to Modern Euclidean Geometries. Hilbert's Model for Euclidean Geometry. Birkhoff's Model for Euclidean Geometry. SMSG Postulates for Euclidean Geometry. Non-Euclidean Geometries.
3. Traveling Together (Neutral Geometry).
Introduction. Preliminary Notions. Congruence Conditions. The Place of Parallels. The Saccheri-Legendre Theorem. The Search for a Rectangle. Summary.
4. One Way to Go (Euclidean Geometry of the Plane).
Introduction. The Parallel Postulate and Some Implications. Congruence and Area. Similarity. Euclidean Results Concerning Circles. Some Euclidean Results Concerning Triangles. More Euclidean Results Concerning Triangles. The Nine-Point Circle. Euclidean Constructions. Summary.
5. Side Trips (Analytic and Transformational Geometry).
Introduction. Analytic Geometry. Transformational Geometry. Analytic Transformations. Inversion. Summary.
6. Other Ways to Go (Non-Euclidean Geometries).
Introduction. A Return to Neutral Geometry: The Angle of Parallelism. The Hyperbolic Parallel Postulate. Hyperbolic Results Concerning Polygons. Area in Hyperbolic Geometry. Showing Consistency: A Model for Hyperbolic Geometry. Classifying Theorems. Elliptic Geometry: A Geometry With No Parallels? Geometry in the Real World. Summary.
7. All Roads Lead To . . . Projective Geometry.
Introduction. The Real Projective Plane. Duality. Perspectivity. The Theorem of Desargues. Projective Transformations. Summary.
Appendix A.
Euclid's Definitions and Postulates Book I.
Appendix B.
Hilbert's Axioms for Euclidean Plane Geometry.
Appendix C.
Birkhoff's Postulates for Euclidean Plane Geometry.
Appendix D.
The SMSG Postulates for Euclidean Geometry.
Appendix E.
Geometer's SketchPad... Scripts for Poincare Model of Hyperbolic Geometry.
Bibliography.
Index.
Historical Background: Axiomatic Systems and their Properties. Finite Geometries. Axioms for Incidence Geometry.
2. Many Ways to Go.
Introduction. Euclid's Geometry and Euclid's Elements. An Introduction to Modern Euclidean Geometries. Hilbert's Model for Euclidean Geometry. Birkhoff's Model for Euclidean Geometry. SMSG Postulates for Euclidean Geometry. Non-Euclidean Geometries.
3. Traveling Together (Neutral Geometry).
Introduction. Preliminary Notions. Congruence Conditions. The Place of Parallels. The Saccheri-Legendre Theorem. The Search for a Rectangle. Summary.
4. One Way to Go (Euclidean Geometry of the Plane).
Introduction. The Parallel Postulate and Some Implications. Congruence and Area. Similarity. Euclidean Results Concerning Circles. Some Euclidean Results Concerning Triangles. More Euclidean Results Concerning Triangles. The Nine-Point Circle. Euclidean Constructions. Summary.
5. Side Trips (Analytic and Transformational Geometry).
Introduction. Analytic Geometry. Transformational Geometry. Analytic Transformations. Inversion. Summary.
6. Other Ways to Go (Non-Euclidean Geometries).
Introduction. A Return to Neutral Geometry: The Angle of Parallelism. The Hyperbolic Parallel Postulate. Hyperbolic Results Concerning Polygons. Area in Hyperbolic Geometry. Showing Consistency: A Model for Hyperbolic Geometry. Classifying Theorems. Elliptic Geometry: A Geometry With No Parallels? Geometry in the Real World. Summary.
7. All Roads Lead To . . . Projective Geometry.
Introduction. The Real Projective Plane. Duality. Perspectivity. The Theorem of Desargues. Projective Transformations. Summary.
Appendix A.
Euclid's Definitions and Postulates Book I.
Appendix B.
Hilbert's Axioms for Euclidean Plane Geometry.
Appendix C.
Birkhoff's Postulates for Euclidean Plane Geometry.
Appendix D.
The SMSG Postulates for Euclidean Geometry.
Appendix E.
Geometer's SketchPad... Scripts for Poincare Model of Hyperbolic Geometry.
Bibliography.
Index.