Brainstorming on

**Review:Tessellations and symmetry in FAPP.**

**ISOMETRIES: Rigid Motions in (or about) the plane.**

Also called "Isometries"

Orientation preservingTranslationsRotationsOrientation reversingReflectionsGlide reflections

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

OrientationReverse

OrientationNo Fixed points Translation Glide reflection Fixed Point(s) Rotation Reflection Using Isometries to create variations of tilings180 degree Rotations

Translations