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Geometry Transformed: Euclidean Plane Geometry Based on Rigid Motions
 
James R. King University of Washington, Seattle, WA
Geometry Transformed
Softcover ISBN:  978-1-4704-6307-6
Product Code:  AMSTEXT/51
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-6443-1
Product Code:  AMSTEXT/51.E
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
Softcover ISBN:  978-1-4704-6307-6
eBook: ISBN:  978-1-4704-6443-1
Product Code:  AMSTEXT/51.B
List Price: $198.00 $148.50
MAA Member Price: $178.20 $133.65
AMS Member Price: $158.40 $118.80
Geometry Transformed
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Geometry Transformed: Euclidean Plane Geometry Based on Rigid Motions
James R. King University of Washington, Seattle, WA
Softcover ISBN:  978-1-4704-6307-6
Product Code:  AMSTEXT/51
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-6443-1
Product Code:  AMSTEXT/51.E
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
Softcover ISBN:  978-1-4704-6307-6
eBook ISBN:  978-1-4704-6443-1
Product Code:  AMSTEXT/51.B
List Price: $198.00 $148.50
MAA Member Price: $178.20 $133.65
AMS Member Price: $158.40 $118.80
  • Book Details
     
     
    Pure and Applied Undergraduate Texts
    Volume: 512021; 258 pp
    MSC: Primary 51; 97; 20

    Many paths lead into Euclidean plane geometry. Geometry Transformed offers an expeditious yet rigorous route using axioms based on rigid motions and dilations. Since transformations are available at the outset, interesting theorems can be proved sooner; and proofs can be connected to visual and tactile intuition about symmetry and motion. The reader thus gains valuable experience thinking with transformations, a skill that may be useful in other math courses or applications. For students interested in teaching mathematics at the secondary school level, this approach is particularly useful since geometry in the Common Core State Standards is based on rigid motions.

    The only prerequisite for this book is a basic understanding of functions. Some previous experience with proofs may be helpful, but students can also learn about proofs by experiencing them in this book—in a context where they can draw and experiment. The eleven chapters are organized in a flexible way to suit a variety of curriculum goals. In addition to a geometrical core that includes finite symmetry groups, there are additional topics on circles and on crystallographic and frieze groups, and a final chapter on affine and Cartesian coordinates. The exercises are a mixture of routine problems, experiments, and proofs.

    This book is published in cooperation with IAS/Park City Mathematics Institute.
    Readership

    Undergraduate and graduate students interested in geometry aligned with Common Core standards (CCSSM).

  • Table of Contents
     
     
    • Chapters
    • Congruence and rigid motions
    • Axioms for the plane
    • Existence and properties of reflections
    • Congruence of triangles
    • Rotation and orientation
    • Half-turns and inequalities in triangles
    • Parallel lines and translations
    • Dilations and similarity
    • Area and its applications
    • Products and patterns
    • Coordinate geometry
  • Reviews
     
     
    • Overall, the book is a valuable one; it is always nice to see a new approach to an old subject, particularly when the material is handled as deftly as it is here. Instructors teaching geometry, or just interested in the subject for their own pleasure, should definitely look at this book.

      Mark Hunacek (Iowa State University), Cambridge University Press
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 512021; 258 pp
MSC: Primary 51; 97; 20

Many paths lead into Euclidean plane geometry. Geometry Transformed offers an expeditious yet rigorous route using axioms based on rigid motions and dilations. Since transformations are available at the outset, interesting theorems can be proved sooner; and proofs can be connected to visual and tactile intuition about symmetry and motion. The reader thus gains valuable experience thinking with transformations, a skill that may be useful in other math courses or applications. For students interested in teaching mathematics at the secondary school level, this approach is particularly useful since geometry in the Common Core State Standards is based on rigid motions.

The only prerequisite for this book is a basic understanding of functions. Some previous experience with proofs may be helpful, but students can also learn about proofs by experiencing them in this book—in a context where they can draw and experiment. The eleven chapters are organized in a flexible way to suit a variety of curriculum goals. In addition to a geometrical core that includes finite symmetry groups, there are additional topics on circles and on crystallographic and frieze groups, and a final chapter on affine and Cartesian coordinates. The exercises are a mixture of routine problems, experiments, and proofs.

This book is published in cooperation with IAS/Park City Mathematics Institute.
Readership

Undergraduate and graduate students interested in geometry aligned with Common Core standards (CCSSM).

  • Chapters
  • Congruence and rigid motions
  • Axioms for the plane
  • Existence and properties of reflections
  • Congruence of triangles
  • Rotation and orientation
  • Half-turns and inequalities in triangles
  • Parallel lines and translations
  • Dilations and similarity
  • Area and its applications
  • Products and patterns
  • Coordinate geometry
  • Overall, the book is a valuable one; it is always nice to see a new approach to an old subject, particularly when the material is handled as deftly as it is here. Instructors teaching geometry, or just interested in the subject for their own pleasure, should definitely look at this book.

    Mark Hunacek (Iowa State University), Cambridge University Press
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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