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.
- 284 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
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Table of contents
- Cover
- Title page
- Copyright
- Contents
- Introduction
- Advice for Students and Less Experienced Geometers
- Information for More Experienced Geometers
- A Chapter Guide for Instructors and Others
- Acknowledgments
- Chapter 1. Congruence and Rigid Motions
- Chapter 2. Axioms for the Plane
- Chapter 3. Existence and Properties of Reflections
- Chapter 4. Congruence of Triangles
- Chapter 5. Rotation and Orientation
- Chapter 6. Half-turns and Inequalities in Triangles
- Chapter 7. Parallel Lines and Translations
- Chapter 8. Dilations and Similarity
- Chapter 9. Area and Its Applications
- Chapter 10. Products and Patterns
- Chapter 11. Coordinate Geometry
- Bibliography
- Index
- Back Cover
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Yes, you can access Geometry Transformed by James R. King in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over 1.5 million books available in our catalogue for you to explore.