Roads to Geometry

ISBN-10: 0131816527
ISBN-13: 9780131816527
Edition: 2nd 1998
List price: $88.00
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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  More...

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Book details

List price: $88.00
Edition: 2nd
Copyright year: 1998
Publisher: Prentice Hall PTR
Publication date: 8/29/1997
Binding: Hardcover
Pages: 447
Size: 6.30" wide x 9.25" long x 0.83" tall
Weight: 1.826
Language: English

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.

Rules of the Road (Axiomatic Systems)
Historical Background: Axiomatic Systems and their Properties. Finite Geometries. Axioms for Incidence Geometry
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
Traveling Together (Neutral Geometry)
Introduction
Preliminary Notions
Congruence Conditions
The Place of Parallels
The Saccheri-Legendre Theorem
The Search for a Rectangle
Summary
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
Side Trips (Analytic and Transformational Geometry)
Introduction
Analytic Geometry
Transformational Geometry
Analytic Transformations
Inversion
Summary
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
All Roads Lead To . . . Projective Geometry
Introduction
The Real Projective Plane
Duality
Perspectivity
The Theorem of Desargues
Projective Transformations
Summary
Euclid's Definitions and Postulates Book I
Hilbert's Axioms for Euclidean Plane Geometry
Birkhoff's Postulates for Euclidean Plane Geometry
The SMSG Postulates for Euclidean Geometry
Geometer's SketchPad Scripts for Poincare Model of Hyperbolic Geometry
Bibliography
Index

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