Monday March 24
Discuss assignment for this week - make note of project and portfolio.
of Isometries - Symmetries
An isometry is a transformation that preserves the distance between
We have discussed four
reflections, rotations, translations, and glide reflections.
The Product of isometries:
The product of two reflections is either a rotation (if the
axes of the reflection intersect) or a translation (if the axes
the reflection are parallel).
demonstration for reflection- one and two reflections
How do we understand objects in space?
How can the Flatlander experience the sphere and space?
Pick up templates to make Platonic
models for next class!
The simplest three dimensional figure has 4 points not all in the same
plane: three point determine a plane- so a fourth point not in that
plane will need "space" to make sense. These four points determine a
Cross sections: Look at the tetrahedron with cross sections :
Triangles, what if the tetrahedron starts through Flatland with an edge
Fold downs- flattened figures: Consider how the cube can be assembled
folded down squares in two different configurations: a cross or a
What does a folded down
torus look like?
A rectangle with opposite sides resulting from cutting the torus open
making a cylinder and then cutting the cylinder along its length.