9780387986500

Geometry

by
  • ISBN13:

    9780387986500

  • ISBN10:

    0387986502

  • Format: Hardcover
  • Copyright: 2000-06-01
  • Publisher: Springer Verlag
  • Purchase Benefits
  • Free Shipping On Orders Over $35!
    Your order must be $35 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
  • Get Rewarded for Ordering Your Textbooks! Enroll Now
List Price: $64.95

Summary

This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, geometrical constructions and finite field extensions, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra. The text is intended for junior- to senior-level mathematics majors. Robin Hartshorne is a professor of mathematics at the University of California at Berkeley, and is the author of Foundations of Projective Geometry (Benjamin, 1967) and Algebraic Geometry (Springer, 1977).

Table of Contents

Introduction 1(6)
Euclid's Geometry
7(58)
A First Look at Euclid's Elements
8(10)
Ruler and Compass Constructions
18(9)
Euclid's Axiomatic Method
27(18)
Construction of the Regular Pentagon
45(6)
Some Newer Results
51(14)
Hilbert's Axioms
65(52)
Axioms of Incidence
66(7)
Axioms of Betweenness
73(8)
Axioms of Congruence for Line Segments
81(9)
Axioms of Congruence for Angles
90(6)
Hilbert Planes
96(8)
Intersection of Lines and Circles
104(8)
Euclidean Planes
112(5)
Geometry over Fields
117(48)
The Real Cartesian Plane
118(10)
Abstract Fields and Incidence
128(7)
Ordered Fields and Betweenness
135(5)
Congruence of Segments and Angles
140(8)
Rigid Motions and SAS
148(10)
Non-Archimedean Geometry
158(7)
Segment Arithmetic
165(30)
Addition and Multiplication of Line Segments
165(10)
Similar Triangles
175
Introduction of Coordinates
166(29)
Area
195(46)
Area in Euclid's Geometry
196(9)
Measure of Area Functions
205(7)
Dissection
212(9)
Quadratura Circuli
221(5)
Euclid's Theory of Volume
226(5)
Hilbert's Third Problem
231(10)
Construction Problems and Field Extensions
241(54)
Three Famous Problems
242(8)
The Regular 17-Sided Polygon
250(9)
Constructions with Compass and Marked Ruler
259(11)
Cubic and Quartic Equations
270(10)
Appendix: Finite Field Extensions
280(15)
Non-Euclidean Geometry
295(140)
History of the Parallel Postulate
296(8)
Neutral Geometry
304(15)
Archimedean Neutral Geometry
319(7)
Non-Euclidean Area
326(8)
Circular Inversion
334(12)
Digression: Circles Determined by Three Conditions
346(9)
The Poincare Model
355(18)
Hyperbolic Geometry
373(15)
Hilbert's Arithmetic of Ends
388(15)
Hyperbolic Trigonometry
403(12)
Characterization of Hilbert Planes
415(20)
Polyhedra
435(46)
The Five Regular Solids
436(12)
Euler's and Cauchy's Theorems
448(11)
Semiregular and Face-Regular Polyhedra
459(10)
Symmetry Groups of Polyhedra
469(12)
Appendix: Brief Euclid 481(6)
Notes 487(8)
References 495(8)
List of Axioms 503(2)
Index of Euclid's Propositions 505(2)
Index 507

Rewards Program

Write a Review