Transformation Geometry: An Introduction to Symmetry is a modern approach to Euclidean Geometry. This study of the automorphism groups of the plane and space gives the classical concrete examples that serve as a meaningful preparation for the standard undergraduate course in abstract algebra. The detailed development of the isometries of the plane is based on only the most elementary geometry and is appropriate for graduate courses for secondary teachers.
Transformation Geometry: An Introduction to Symmetry is a modern approach to Euclidean Geometry. This study of the automorphism groups of the plane and space gives the classical concrete examples that serve as a meaningful preparation for the standard undergraduate course in abstract algebra. The detailed development of the isometries of the plane is based on only the most elementary geometry and is appropriate for graduate courses for secondary teachers.
Contents: Introduction.- Properties of Transformations.- Translations and Halfturns.- Reflections.- Congruence.- The Product of Two Reflections.- Even Isometries.- Classification of Plane Isometries.- Equations for Isometries.- The Seven Frieze Groups.- The Seventeen Wallpaper Groups.- Tessellations.- Similarities on the Plane.- Classical Theorems.- Affine Transformations.- Transformations on Three-Space.- Space and Symmetry.- Hints and Answers.- Notation Index.- Index.
Contents: Introduction.- Properties of Transformations.- Translations and Halfturns.- Reflections.- Congruence.- The Product of Two Reflections.- Even Isometries.- Classification of Plane Isometries.- Equations for Isometries.- The Seven Frieze Groups.- The Seventeen Wallpaper Groups.- Tessellations.- Similarities on the Plane.- Classical Theorems.- Affine Transformations.- Transformations on Three-Space.- Space and Symmetry.- Hints and Answers.- Notation Index.- Index.
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