Thursday,  September 29
Brainstorming on Project Proposal Guidelines and Suggestions
• Review:Tessellations and symmetry in FAPP.

• ISOMETRIES: Rigid Motions in (or about) the plane.
Also called "Isometries"
• 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.

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

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