Geometry: The Line and the Circle
by Maureen T. Carroll, Elyn Rykken
Publisher: AMS/MAA Press
Book Details
| Print ISBN | 9781470448431 |
| eText ISBN | 9781470450632 |
| Publisher | AMS/MAA Press |
| Publishing Year | 2018 |
| Language | English |
| Pages | 480 |
Geometry: The Line and the Circle is an undergraduate textbook by Maureen T. Carroll and Elyn Rykken, published by AMS/MAA Press. Designed for upper-level survey or axiomatic geometry courses, the book links Euclidean and non-Euclidean geometry within a historical context.
The line and the circle serve as unifying elements across spherical, hyperbolic, taxicab, finite affine, and projective geometries. These central forms guide reader analysis of fundamental questions regarding straight lines, parallel lines, distance, and area.
Alongside extensive analysis of Euclid's Elements, the volume provides hundreds of problems and is supported by a companion book of laboratory projects using GeoGebra.
Table of Contents
Chapter 1: The Line and the Circle
Chapter 2: Euclid’s Elements: Definitions and Axioms
Chapter 3: Book I of Euclid’s Elements: Neutral Geometry
Chapter 4: Spherical Geometry
Chapter 5: Taxicab Geometry
Chapter 6: Hilbert and Gödel
Chapter 7: Book I: Non-Neutral Geometry
Chapter 8: Book II: Geometric Algebra
Chapter 9: Book VI: Similarity
Chapter 10: Book III: Circles
Chapter 11: Book IV: Circles & Polygons
Chapter 12: Models for the Hyperbolic Plane
Chapter 13: Axiomatic Hyperbolic Geometry
Chapter 14: Finite Geometries
Chapter 15: Isometries
Chapter 16: Constructibility
Chapter Appendix A: Euclid’s Definitions and Axioms
Chapter Appendix B: Euclid’s Propositions
Chapter Appendix C: Visual Guide to Euclid’s Propositions
Chapter Appendix D: Euclid’s Proofs
Chapter Appendix E: Hilbert’s Axioms for Plane Euclidean Geometry
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