Geometry transformed : Euclidean plane geometry based on rigid motions
Author(s)
Bibliographic Information
Geometry transformed : Euclidean plane geometry based on rigid motions
（The Sally series, . Pure and applied undergraduate texts ; 51）
American Mathematical Society, c2021
- : pbk
Available at 5 libraries
Note
"Institute for Advanced Study. Park City Mathematics Institute."
Includes bibliographical references (p. 253) and index
Description and Table of Contents
Description
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.
Table of Contents
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
Bibliography
Index
by "Nielsen BookData"