Methods of Geometry,9780471251835

Methods of Geometry

by
Edition: 1st
ISBN13: 9780471251835
ISBN10: 0471251836
Format: Hardcover
Pub. Date: 2000-01-10
Publisher(s): Wiley-Interscience
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Summary

An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

Author Biography

JAMES T. SMITH, PhD, is Professor of Mathematics at San Francisco State University.

Table of Contents

Preface xi
About the author xv
Introduction
1(18)
Episodes
2(7)
Advanced geometry
9(4)
This book
13(3)
Reading about geometry
16(1)
Projects
17(2)
Foundations
19(34)
Geometry as applied mathematics
20(3)
Need for rigor
23(3)
Axiomatic method
26(3)
Euclid's Elements
29(4)
Coordinate geometry
33(2)
Foundation problem
35(2)
Parallel axiom
37(2)
Firm foundations
39(3)
Geometry as pure mathematics
42(8)
Exercises and projects
50(3)
Elementary Euclidean geometry
53(74)
Incidence geometry
55(2)
Ruler axiom and its consequences
57(3)
Pasch's axiom and the separation theorems
60(4)
Angles and the protractor axioms
64(3)
Congruence
67(4)
Perpendicularity
71(5)
Parallel axiom and related theorems
76(5)
Area and Pythagoras' theorem
81(8)
Similarity
89(3)
Polyhedral volume
92(8)
Coordinate geometry
100(6)
Circles and spheres
106(4)
Arcs and trigonometric functions
110(9)
π
119(8)
Exercises on elementary geometry
127(30)
Exercises on the incidence and ruler axioms
128(2)
Exercises related to Pasch's axiom
130(3)
Exercises on congruence and perpendicularity
133(2)
Exercises involving the parallel axiom
135(2)
Exercises on similarity and Pythagoras' theorem
137(3)
Exercises on circles and spheres, part 1
140(3)
Exercises on area
143(3)
Exercises on volume
146(2)
Exercises on circles and spheres, part 2
148(3)
Exercises on coordinate geometry
151(6)
Some triangle and circle geometry
157(70)
Four concurrence theorems
158(4)
Menelaus' theorem
162(3)
Desargues' theorem
165(6)
Ceva's theorem
171(6)
Trigonometry
177(9)
Vector products
186(7)
Centroid
193(3)
Orthocenter
196(3)
Incenter and excenters
199(5)
Euler line and Feuerbach circle
204(7)
Exercises
211(16)
Plane isometries and similarities
227(68)
Transformations
232(8)
Isometries
240(7)
Reflections
247(4)
Translations
251(3)
Rotations
254(4)
Structure theorem
258(3)
Glide reflections
261(1)
Isometries and orthogonal matrices
262(5)
Classifying isometries
267(9)
Similarities
276(5)
Exercises
281(14)
Three dimensional isometries and similarities
295(32)
Isometries
296(6)
Reflections
302(4)
Translations and rotations
306(3)
Glide and rotary reflections
309(3)
Classifying isometries
312(3)
Similarities
315(2)
Exercises
317(10)
Symmetry
327(96)
Polygonal symmetry
336(8)
Friezes
344(11)
Wallpaper ornaments
355(26)
Polyhedra
381(26)
Exercises
407(16)
Appendix A Equivalence relations 423(2)
Appendix B Least upper bound principle 425(4)
Appendix C Vector and matrix algebra 429(14)
Bibliography 443(20)
Index 463

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