Designed for junior-senior level mathematics majors, including those who plan to teach secondary mathematics. Chapters include lists of suggested sources for applications and/or related topics in areas such as art and history.
- Chapter 1: describes axiomatic systems and presents finite geometry examples.
- Chapter 2: explores Euclid’s geometry and basic ideas of non-Euclidean geometry with special emphasis on hyperbolic geometry.
- Chapter 3: introduces symmetry and isometries via hands-on explorations, and then formally presents transformations of the Euclidean plane, using matrix representations.
- Chapter 4: presents plane projective geometry first synthetically, and then analytically by generalizing the transformation coverage of Chapter 3.
- Chapter 5: explores chaos theory and fractal geometry, stressing the self-similar nature of fractals and the role of transformations from Chapter 3 in their generation.
A. Errata for Second Edition
B. Explorations with Dynamic Geometry Software
These guided activities use the interactive capabilities of dynamic geometry software (specifically, Cabri Geometry and Geometer’s Sketchpad ) to supplement and enhance many of the topics covered in the text. Each exploration includes a list of required equipment and detailed directions (in parallel versions for the two softwares) designed for independent student use.