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Thinking Geometrically: A Survey of Geometries
 
Thinking Geometrically
MAA Press: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-1-93951-208-6
Product Code:  TEXT/26
List Price: $79.00
MAA Member Price: $59.25
AMS Member Price: $59.25
eBook ISBN:  978-1-61444-619-4
Product Code:  TEXT/26.E
List Price: $69.00
MAA Member Price: $51.75
AMS Member Price: $51.75
Hardcover ISBN:  978-1-93951-208-6
eBook: ISBN:  978-1-61444-619-4
Product Code:  TEXT/26.B
List Price: $148.00 $113.50
MAA Member Price: $111.00 $85.13
AMS Member Price: $111.00 $85.13
Thinking Geometrically
Click above image for expanded view
Thinking Geometrically: A Survey of Geometries
MAA Press: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-1-93951-208-6
Product Code:  TEXT/26
List Price: $79.00
MAA Member Price: $59.25
AMS Member Price: $59.25
eBook ISBN:  978-1-61444-619-4
Product Code:  TEXT/26.E
List Price: $69.00
MAA Member Price: $51.75
AMS Member Price: $51.75
Hardcover ISBN:  978-1-93951-208-6
eBook ISBN:  978-1-61444-619-4
Product Code:  TEXT/26.B
List Price: $148.00 $113.50
MAA Member Price: $111.00 $85.13
AMS Member Price: $111.00 $85.13
  • Book Details
     
     
    AMS/MAA Textbooks
    Volume: 262015; 559 pp

    This is a well written and comprehensive survey of college geometry that would serve a wide variety of courses for both mathematics majors and mathematics education majors. Great care and attention is spent on developing visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. Students with less mathematical preparation than upper-division mathematics majors can successfully study the topics needed for the preparation of high school teachers.

    There is a multitude of exercises and projects in those chapters developing all aspects of geometric thinking for these students as well as for more advanced students. These chapters include Euclidean Geometry, Axiomatic Systems and Models, Analytic Geometry, Transformational Geometry, and Symmetry. Topics in the other chapters, including Non-Euclidean Geometry, Projective Geometry, Finite Geometry, Differential Geometry, and Discrete Geometry, provide a broader view of geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics.

    The text is self-contained, including appendices with the material in Euclid's first book and a high school axiomatic system as well as Hilbert's axioms. Appendices give brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters. While some chapters use the language of groups, no prior experience with abstract algebra is presumed. The text will support an approach emphasizing dynamical geometry software without being tied to any particular software.

    Ancillaries:

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Euclidean Geometry
    • Chapter 2. Axiomatic Systems
    • Chapter 3. Analytic Geometry
    • Chapter 4. Non-Euclidean Geometries
    • Chapter 5. Transformational Geometry
    • Chapter 6. Symmetry
    • Chapter 7. Projective Geometry
    • Chapter 8. Finite Geometries
    • Chapter 9. Differential Geometry
    • Chapter 10. Discrete Geometry
    • Chapter 11. Epilogue
    • A. Definitions, Postulates, Common Notions, and Propositions from Book I of Euclid’s Elements
    • B. SMSG Axioms for Euclidean Geometry
    • C. Hilbert’s Axioms for Euclidean Plane Geometry
    • D. Linear Algebra Summary
    • E. Multivariable Calculus Summary
    • F. Elements of Proofs
  • Additional Material
     
     
  • Reviews
     
     
    • This also visually very appealing book offers a wealth of geometric information together with the historical background. The author takes the reader onto a long and engrossing journey to 11 well-selected basic sites of classical and modern geometry. Geometric intuition and facility in proofs are developed. Visualization by the use of dynamic geometry software is included in many exercises and projects.

      Zentrallblatt
  • 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: 262015; 559 pp

This is a well written and comprehensive survey of college geometry that would serve a wide variety of courses for both mathematics majors and mathematics education majors. Great care and attention is spent on developing visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. Students with less mathematical preparation than upper-division mathematics majors can successfully study the topics needed for the preparation of high school teachers.

There is a multitude of exercises and projects in those chapters developing all aspects of geometric thinking for these students as well as for more advanced students. These chapters include Euclidean Geometry, Axiomatic Systems and Models, Analytic Geometry, Transformational Geometry, and Symmetry. Topics in the other chapters, including Non-Euclidean Geometry, Projective Geometry, Finite Geometry, Differential Geometry, and Discrete Geometry, provide a broader view of geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics.

The text is self-contained, including appendices with the material in Euclid's first book and a high school axiomatic system as well as Hilbert's axioms. Appendices give brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters. While some chapters use the language of groups, no prior experience with abstract algebra is presumed. The text will support an approach emphasizing dynamical geometry software without being tied to any particular software.

Ancillaries:

  • Chapters
  • Chapter 1. Euclidean Geometry
  • Chapter 2. Axiomatic Systems
  • Chapter 3. Analytic Geometry
  • Chapter 4. Non-Euclidean Geometries
  • Chapter 5. Transformational Geometry
  • Chapter 6. Symmetry
  • Chapter 7. Projective Geometry
  • Chapter 8. Finite Geometries
  • Chapter 9. Differential Geometry
  • Chapter 10. Discrete Geometry
  • Chapter 11. Epilogue
  • A. Definitions, Postulates, Common Notions, and Propositions from Book I of Euclid’s Elements
  • B. SMSG Axioms for Euclidean Geometry
  • C. Hilbert’s Axioms for Euclidean Plane Geometry
  • D. Linear Algebra Summary
  • E. Multivariable Calculus Summary
  • F. Elements of Proofs
  • This also visually very appealing book offers a wealth of geometric information together with the historical background. The author takes the reader onto a long and engrossing journey to 11 well-selected basic sites of classical and modern geometry. Geometric intuition and facility in proofs are developed. Visualization by the use of dynamic geometry software is included in many exercises and projects.

    Zentrallblatt
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.