Modern Geometries

ISBN-10: 0534351883

ISBN-13: 9780534351885

Edition: 5th 1998 (Revised)

Authors: James R. Smart

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Description:

This comprehensive, best-selling text focuses on the study of many different geometries -- rather than a single geometry -- and is thoroughly modern in its approach. Each chapter is essentially a short course on one aspect of modern geometry, including finite geometries, the geometry of transformations, convexity, advanced Euclidian geometry, inversion, projective geometry, geometric aspects of topology, and non-Euclidean geometries. This edition reflects the recommendations of the COMAP proceedings on Geometry's Future, the NCTM standards, and the Professional Standards for Teaching Mathematics. References to a new companion text, Active Geometry by David A. Thomas encourage students to explore the geometry of motion through the use of computer software. Using Active Geometry at the beginning of various sections allows professors to give students a somewhat more intuitive introduction using current technology before moving on to more abstract concepts and theorems.
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Book details

List price: $299.95
Edition: 5th
Copyright year: 1998
Publisher: Brooks/Cole
Publication date: 12/15/1997
Binding: Hardcover
Pages: 480
Size: 6.75" wide x 9.75" long x 1.00" tall
Weight: 1.584
Language: English

Sets of Axioms and Finite Geometries
Introduction to Geometry
Development of Modern Geometries
Introduction to Finite Geometries
Four-Line and Four-Point Geometries
Finite Geometries of Fano and Young
Finite Geometries of Pappus and Desargues
Other Finite Geometries
Geometric Transformations Introduction To Transformations
Groups of Transformations
Euclidean Motions of the Plane
Sets of Equations for Motions of the Plane
Applications of Transformations in Computer Graphics
Properties of the Group of Euclidean Motions
Motions and Graphics of Three-Space
Similarity Transformations
Introduction to the Geometry of Fractals and Fractal Dimension
Examples and Applications of Fractals
Convexity Basic Concepts
Convex Sets and Supporting Lines
Convex Bodies in Two-Space
Convex Bodies in Three-Space
Convex Hulls
Width of a Set
Helly''s Theorem and Applications
Modern Euclidean Geometry, Theory, And Applications
Fundamental Concepts and Theorems
Some Theorems Leading to Modern Synthetic Geometry
The Nine-Point Circle and Early Nineteenth-Century Synthetic Geometry
Isogonal Conjugates
Recent Synthetic Geometry of the Triangle
Golden Ratio, Tessellations, Packing Problems and Pick''s Theorem
Extremum Problems, Geometric Probability, Fuzzy Sets, and Bezier Curves
Constructions
The Philosophy of Constructions
Constructible Numbers
Constructions in Advanced Euclidean Geometry
Constructions and Impossibility Proofs
Constructions by Paper Folding and by Use of Computer Software
Constructions with Only One Instrument
The Transformation Of Inversion
Basic Concepts
Additional Properties and Invariants under Inversion
The Analytic Geometry of Inversion
Some Applications of Inversion
Projective Geometry
Fundamental Concepts
Postulational Basis for Projective Geometry
Duality and Some Consequences
Harmonic Sets
Projective Transformations
Homogenous Coordinates
Equations for Projective Transformations
Special Projectivities
Conics
Constructions of Conics
Geometric Introduction To Topological Transformations
Topological Transformations
Simple Closed Curves
Invariant Points and Networks
Introduction to the Topology of Surfaces
Euler''s Formula and the Map-Coloring Problem
Non-Euclidean Geometries
Foundations of Euclidean and Non-Euclidean Geometries
Introduction to Hyperbolic Geometry
Ideal Points and Omega Triangles
Quadrilaterals and Triangles
Pairs of Lines and Area of Triangular Regions
Curves
Elliptic Geometry
Consistency; Other Modern Geometries
Selected Ideas From Logic
Review Of Euclidean Geometry
First Twenty-Eight Propositions Of Euclid
Hilbert''s Axioms
Birkhoff''s Postulates
Illustrations Of Basic Euclidean Constructions
Bibliography
Answers To Selected Exercises
Index
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