Thursday,  September 29
  Brainstorming on Project Proposal Guidelines and Suggestions
  • Orientation preserving
  • Translations
  • Rotations
  • Orientation reversing
  • Reflections
  • Glide reflections

  • Classification of Isometries
    Video : Isometries
    The video introduced the four isometries we have discussed:
    reflections, rotations, translations, and glide reflections.

    • The product of two reflections is either a rotation (if the axes of the reflection intersect)  or a translation (if the axes of the reflection are parallel).

    Wingeometry demonstration for reflection- one and two reflections
    What about 3 reflections? 

    • Every plane isometry is the product of at most three reflections.
    discuss basic idea:
    • Recall: Reflection is related to "perpendicular bisector" of PP'
    • With a triangle the 3 vertices ABC -> A'B'C' may be related to at most 3 lines of reflection.

    The product of two reflections is either a rotation or translation.

    The product of three reflections is either a reflection or glide reflection

    How to figure out what isometry you have.... match features.

    No Fixed points Translation Glide reflection
    Fixed Point(s) Rotation Reflection

  • Using Isometries to create variations of tilings
  • 180 degree Rotations