• Review:Tessellations and symmetry in FAPP.
  

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

Orientation preserving

Translations

Rotations

Orientation reversing

Reflections

Glide reflections

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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).

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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

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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

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Using Isometries to create variations of tilings

180 degree Rotations
Translations

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