Euclidean and Non-Euclidean Geometries

Name: Euclidean and Non-Euclidean Geometries
Availability: OutOfStock
ISBN: 9780130337177

ISBN-10: 013033717X

ISBN-13: 9780130337177

Edition: 2002

Authors: Helena Noronha

List price: $103.00

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Description:

This book develops a self-contained treatment of classical Euclidean geometry through both axiomatic and analytic methods. Concise and well organized, it prompts readers to prove a theorem yet provides them with a framework for doing so. Chapter topics cover neutral geometry, Euclidean plane geometry, geometric transformations, Euclidean 3-space, Euclidean n-space; perimeter, area and volume; spherical geometry; hyperbolic geometry; models for plane geometries; and the hyperbolic metric.

Book details

List price: $103.00
Copyright year: 2002
Publisher: Prentice Hall PTR
Publication date: 7/11/2001
Binding: Hardcover
Pages: 409
Size: 6.25" wide x 9.00" long x 0.75" tall
Weight: 1.430




Neutral Geometry


Introduction


Axioms of Incidence and Betweenness


Convex Sets


Measuring Segments and Angles


Congruence of Triangles


The Circle


Principles of Continuity


The Basic Geometric Constructions



Euclidean Plane Geometry


Euclid's Fifth Postulate


Euclidean Triangles


Similar Triangles


Euclidean Circles


Trigonometric Functions


Euclidean Constructions



Geometric Transformations


Rigid Motions


Similarities


Inversions


Coordinate Systems


Appendix



Euclidean 3-Space


Axiom System for 3-Dimensional Geometry


Perpendicular Lines and Planes


Rigid Motions in 3-Space


Vectors in 3-Space



Euclidean n-Space


The n-Space


Basis and Change of Coordinates


Linear Transformations


Orthogonal Transformations


Orthogonal transformations ofR 2 andR 3. Orientation



Perimeter, Area and Volume


Perimeter and Circumference


Area of Polygonal Regions


Area of Circles


Volumes



Spherical Geometry


Arc Length


Metric Spaces


Spherical Distance and Its Isometries


Geodesics and Triangles on Spheres


Conformal Maps


Appendix



Hyperbolic Geometry


Introduction


Neutral Geometry Revisited


The Hyperbolic Parallel Postulate


Classification of Parallels


The Angle of Parallelism


Defect of Hyperbolic Triangles



Models for Plane Geometries


Introduction


The Poincarï¿½ Models


A Note on Elliptic Geometry



The Hyperbolic Metric


Introduction


The Complex Plane


Analytic Functions


Geometric Transformations


Classification of Isometries


The Hyperbolic Metric


Hyperbolic Triangles


Hyperbolic Circles


List of Axioms


Index