A Course In Modern Geometries, Second Edition, Springer
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
- 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.
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.
A. Errata for Second Edition
C. Web Sites for Other Geometry Resources: