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Geometry: The Line and the Circle
 
Maureen T. Carroll University of Scranton, Scranton, PA
Elyn Rykken Muhlenberg College, Allentown, PA
Geometry: The Line and the Circle
MAA Press: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-1-4704-4843-1
Product Code:  TEXT/44
List Price: $109.00
MAA Member Price: $81.75
AMS Member Price: $81.75
eBook ISBN:  978-1-4704-5063-2
Product Code:  TEXT/44.E
List Price: $99.00
MAA Member Price: $74.25
AMS Member Price: $74.25
Hardcover ISBN:  978-1-4704-4843-1
eBook: ISBN:  978-1-4704-5063-2
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
Geometry: The Line and the Circle
Click above image for expanded view
Geometry: The Line and the Circle
Maureen T. Carroll University of Scranton, Scranton, PA
Elyn Rykken Muhlenberg College, Allentown, PA
MAA Press: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-1-4704-4843-1
Product Code:  TEXT/44
List Price: $109.00
MAA Member Price: $81.75
AMS Member Price: $81.75
eBook ISBN:  978-1-4704-5063-2
Product Code:  TEXT/44.E
List Price: $99.00
MAA Member Price: $74.25
AMS Member Price: $74.25
Hardcover ISBN:  978-1-4704-4843-1
eBook ISBN:  978-1-4704-5063-2
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
  • Book Details
     
     
    AMS/MAA Textbooks
    Volume: 442018; 480 pp
    MSC: 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 upper-level survey or axiomatic course in geometry. Starting with Euclid's Elements, the book connects topics in Euclidean and non-Euclidean 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, non-Euclidean 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:

    Readership

    Undergraduate 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: 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 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
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
    Examination Copy – for faculty considering an AMS textbook for a course
    Accessibility – to request an alternate format of an AMS title
Volume: 442018; 480 pp
MSC: 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 upper-level survey or axiomatic course in geometry. Starting with Euclid's Elements, the book connects topics in Euclidean and non-Euclidean 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, non-Euclidean 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:

Readership

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: 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 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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.