Thursday,  February 24

Pre-screening comment on President Summers (Harvard), women and science: President's letter to faculty.
Association for Women in Mathematics's response to Harvard President Lawrence Summers' remarks
Letter from the President of the Anita Borg Institute for Women and Technology: Telle Whitney responds to Lawrence Summers.

Review of Discussion So Far on Classification of Isometries
Video : Isometries
The video introduces the four isometries we have discussed:
reflections, rotations, translations, and glide reflections.

It shows 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).

We saw this also with a Wingeometry demonstration for reflection- one and two reflections

The video shows that
 Any plane isometry  is either a reflection or  the product of two or three reflections.
Two reflections = rotation or translation.
What about 3 reflections? 

Three reflections = reflection or glide reflection
Visual Proof discussion from Math 371 (HSU Geometry Course): Key idea- The product of two reflections is "flexible."

Comment on Symmetry  in Music and Sound: (another dimension?)

Translation   .... by an octave, relative position-- chords
Rotation: thirteen notes in "chromatic" scale
Glide Reflection
Visualizations of music - Examples:
Notation: Conventional music notation:  The mozart viewer

Windows media player.

Space: How do we understand objects in space?
How can the Flatlander experience the sphere and space?
Pick up templates to make Platonic solid models for next class!
Recall assignment: Make a torus with 2 and 1 piece!

Cross sections: Look at the octahedron with cross sections : squares, rectangles, triangles and hexagons depending on how the octahedron passes through the plane.

Shadows: Recall our previous class activity when we considered how the octhedron might case shadows.

Fold downs- flattened figures: Consider how the cube can be assembled from folded down squares in two different configurations: a cross or a "zig-zag."

What does a folded down flattened 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.

    A torus


analogue...  point... line.... polygon.... polyhedron......