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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.
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