Thursday, September 29
Brainstorming on Project Proposal Guidelines and Suggestions
- Review:Tessellations and symmetry in FAPP.
- ISOMETRIES: Rigid Motions in (or about)
Also called "Isometries"
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?
discuss basic idea:
Every plane isometry is the
product of at most three reflections.
- 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
Using Isometries to create variations of tilings
180 degree Rotations