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
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
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.
C. Web Sites for Other Geometry Resources:
Disclaimer
Disclaimer