Tuesday,  September 29
Comment on Project  Proposals  and  portfolio sample entries.
Comment on Symmetry  in Music and Sound:
we discussed
Translation   .... by an octave, relative position-- chords
Reflection
Rotation: thirteen notes in "chromatic" scale
Glide Reflection

Space: How do we understand objects in space?
How can the Flatlander experience the sphere and space?

Try making a torus with 2 and 1 piece!

Cross sections: We looked at the cube with cross sections : squares, rectangles, triangles and hexagons depending on how the square passes through the plane.

Shadows: We looked at how the cube might case shadows that were square, rectangular or hexagonal,

Fold downs- flattened figures: we saw how the cube cube be assembled from folded down squares in two different configurations: a cross or a "zig-zag." [Insert pictures?]

analogue...  point... line.... polygon.... polyhedron......
• Some Issues we'll consider in space:
• Polyhedra and symmetry.
• Historical Note on Kepler.
• Platonic (regular convex polyhedra) and Archimedean (semiregular convex) Solids- on the web!
• Why are there only 5? We looked at the possible ways to put a single regular polygon together with more of the same to make a spatial "cap" about a single vertex. This involved equilateral triangles (3,4, or 5), squares (3) or pentagons (3).
• This showed that there were at most five vertex caps possible. These actually do work to make

•  The 5 Platonic Solids
• Regular polygons around a vertex.
• All vertices are "the same"
• We worked on the activity in counting vertices, edges, and faces for the platonic solids to become more familiar with them.
• The Archimedean  Solids:
•  The 13 Archimedean Solids

• Symmetries (Isometries) in the plane compared to those in space- an introduction:
• Translations
• Rotations: Center point - central axis
• Reflection :  across line - across plane
• Symmetries of the cube:
• Rotations
• reflections
• rotation- reflection
• Isometries in space: products of reflections in space:
• Rotations and translations
• Applications to dance