Geometric Transformations of the Plane

The words geometric transformation, if taken out of context, mean neither more nor less than a function that maps one set of geometric objects on another. However, those transformtaions that are worth studying have special properties, for example, like forming a group, preserving distances or angles. Various geometries can be defined as a study of invariants under specific groups of (geometric) transformations. Geometric transformations also provide powerful tools for solving geometric problems.

Geometric Transformations

• Plane Isometries
  • Reflection in Point
  • Reflection in Line
    • Geometric Problems by Reflection
  • Translation Transform
  • Product of Rotations
    • Rotation Transform
  • Glide Reflection
• Affine Transformations (definition)
  • Iterated Function Systems
  • Homothety
    • Geometric Problems by Homothety
  • Shearing
  • Spiral Similarity
    • Construction of the center of spiral similarility
• Inversion
  • Stereographic Projection and Inversion
  • Möbius Transformations
• Projective transformation

References

1. H. S. M. Coxeter, Introduction to Geometry, John Wiley & Sons, 1961
2. C. Dodge, Euclidean Geometry and Transformations, Dover, 2004
3. H. Eves, A Survey of Geometry, Allyn and Bacon, 1972
4. D. Pedoe, Geometry: A Comprehensive Course, Dover, 1988
5. I. M. Yaglom, Geometric Transformations I, II, III, MAA, 1962

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Copyright © 1996-2012 Alexander Bogomolny