Geometry transformed : euclidean plane geometry based on rigid motions
Material type:
TextSeries: Pure and applied undergraduate texts ; 51 | The Sally seriesPublication details: India : Universities Press, 2025. Description: xxii, 258 pages : illustrations (some color) ; 26 cmISBN: 9789349750159Subject(s): Euclid's Elements | Geometry, Plane | Rigidity (Geometry) | Real and complex geometry -- Elementary problems in Euclidean geometries | Analytic and descriptive geometry | Group theory and generalizationsDDC classification: 514.12 Online resources: Table of Contents | Reviews Summary: 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.
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
NBHM Books
|
SMS Library | 514.12 KIN-G (Browse shelf(Opens below)) | Available | N496 |
Includes bibliographical references and index.
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).
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