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Hardcover ISBN:  9781470448431 
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AMS Member Price:  $156.00 $118.88 
Sale Price:  $135.20 $103.03 
Hardcover ISBN:  9781470448431 
Product Code:  TEXT/44 
List Price:  $109.00 
MAA Member Price:  $81.75 
AMS Member Price:  $81.75 
Sale Price:  $70.85 
eBook ISBN:  9781470450632 
Product Code:  TEXT/44.E 
List Price:  $99.00 
MAA Member Price:  $74.25 
AMS Member Price:  $74.25 
Sale Price:  $64.35 
Hardcover ISBN:  9781470448431 
eBook ISBN:  9781470450632 
Product Code:  TEXT/44.B 
List Price:  $208.00 $158.50 
MAA Member Price:  $156.00 $118.88 
AMS Member Price:  $156.00 $118.88 
Sale Price:  $135.20 $103.03 

Book DetailsAMS/MAA TextbooksVolume: 44; 2018; 480 ppMSC: Primary 51
Geometry: The Line and the Circle is an undergraduate text with a strong narrative that is written at the appropriate level of rigor for an upperlevel survey or axiomatic course in geometry. Starting with Euclid's Elements, the book connects topics in Euclidean and nonEuclidean geometry in an intentional and meaningful way, with historical context.
The line and the circle are the principal characters driving the narrative. In every geometry considered—which include spherical, hyperbolic, and taxicab, as well as finite affine and projective geometries—these two objects are analyzed and highlighted. Along the way, the reader contemplates fundamental questions such as: What is a straight line? What does parallel mean? What is distance? What is area?
There is a strong focus on axiomatic structures throughout the text. While Euclid is a constant inspiration and the Elements is repeatedly revisited with substantial coverage of Books I, II, III, IV, and VI, nonEuclidean geometries are introduced very early to give the reader perspective on questions of axiomatics. Rounding out the thorough coverage of axiomatics are concluding chapters on transformations and constructibility. The book is compulsively readable with great attention paid to the historical narrative and hundreds of attractive problems.
Ancillaries:
ReadershipUndergraduate students interested in geometry.

Table of Contents

Chapters

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: NonNeutral 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 18. Constructibility

Appendix A. Euclid’s definitions and axioms

Appendix B. Euclid’s propositions

Appendix C. Visual guide to Euclid’s propositions

Appendix D. Euclid’s proofs

Appendix E. Hilbert’s axioms for plane Euclidean geometry


Additional Material

Reviews

A fun and masterful road to learning what geometry is actually about. This is likely an ideal text for use in training secondary level teachers who will teach this glorious subject...From constructions to proofs of results to the larger meaning of these results within the overarching context of Geometry, this text is there to guide students and assist them in constructing their own mastery of the subject. It is a beautiful text with real depth and detail and will be of great value to anyone who wishes to know "Just what is geometry about, after all is said and done?". Highly recommended!
Jeff Ibbotson, MAA Reviews


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Geometry: The Line and the Circle is an undergraduate text with a strong narrative that is written at the appropriate level of rigor for an upperlevel survey or axiomatic course in geometry. Starting with Euclid's Elements, the book connects topics in Euclidean and nonEuclidean geometry in an intentional and meaningful way, with historical context.
The line and the circle are the principal characters driving the narrative. In every geometry considered—which include spherical, hyperbolic, and taxicab, as well as finite affine and projective geometries—these two objects are analyzed and highlighted. Along the way, the reader contemplates fundamental questions such as: What is a straight line? What does parallel mean? What is distance? What is area?
There is a strong focus on axiomatic structures throughout the text. While Euclid is a constant inspiration and the Elements is repeatedly revisited with substantial coverage of Books I, II, III, IV, and VI, nonEuclidean geometries are introduced very early to give the reader perspective on questions of axiomatics. Rounding out the thorough coverage of axiomatics are concluding chapters on transformations and constructibility. The book is compulsively readable with great attention paid to the historical narrative and hundreds of attractive problems.
Ancillaries:
Undergraduate students interested in geometry.

Chapters

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: NonNeutral 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 18. Constructibility

Appendix A. Euclid’s definitions and axioms

Appendix B. Euclid’s propositions

Appendix C. Visual guide to Euclid’s propositions

Appendix D. Euclid’s proofs

Appendix E. Hilbert’s axioms for plane Euclidean geometry

A fun and masterful road to learning what geometry is actually about. This is likely an ideal text for use in training secondary level teachers who will teach this glorious subject...From constructions to proofs of results to the larger meaning of these results within the overarching context of Geometry, this text is there to guide students and assist them in constructing their own mastery of the subject. It is a beautiful text with real depth and detail and will be of great value to anyone who wishes to know "Just what is geometry about, after all is said and done?". Highly recommended!
Jeff Ibbotson, MAA Reviews