Thursday, February 17
Finish FAPP Tape on Symmetry
Using Symmetries to create variations of tilings
180 degree Rotations
World of Escher
ISOMETRIES: Rigid Motions in (or about)
the plane. Also called "Isometries"
Classification of Isometries
prepare for Video : Isometries (show video on Tuesday)
The video introduces the four isometries we have discussed:
reflections, rotations, translations, and glide reflections.
Show that 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?
isometry is either a reflection or the product of two or three
discuss basic idea:
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.
Two reflections = rotation or translation.
Three reflections = reflection or glide reflection
How to figure out what isometry you have.... match features.
|No Fixed points
Space: How do we understand objects in space?
How can the Flatlander experience the sphere and space?
fold downs- flattened figures
analogue... point... line.... polygon.... polyhedron......
- Some Issues we'll consider in space:
Platonic (regular convex polyhedra) Solids
Why are there only 5?
- Regular polygons around a vertex.
All vertices are "the same".
Symmetries (Isometries) in the plane compared to those in space- an introduction:
Rotations: Center point - central axis
Reflection : across line - across plane
- Symmetries of the cube:
- Isometries in space: products of reflections in space:
Rotations and translations
Applications to dance