444 Home Page

1. Week 9/30-10/04

2. Week 10/07-11

3. Week 10/14-18

4. Week 10/21-25

5. Week 10/28-11/1

6. Week 11/04-08

7. Week 11/11-15

8. Week 11/18-22

9. Week 11/25-29

10. Week 12/02-06

11. Week 12/09-13

Monday 11/25 444

• Assignment 8A and Assignment 8B due.
• Assignment 9 Due Monday 12/02
• Statement of Napoleon's Theorem for Assignment 9.
• Wallpaper Groups - concepts of transformation group, symmetry group, basic unit (fundamental domain) of a transformation group.

Web Resources : Some very good material on symmetry in general and wallpaper groups in particulat is on the web.

• The Geometry Center Symmetry page has detailed explanations and software.
• David Joyce's Wallpaper Groups
• Java software Escher Web Sketch
• 16 of the 17 groups in traditional Japanese patterns
• Some animated patterns

Wednesday 11/27 444

Relations among tetrahedra, cubes and octahedra

Cube decomposes into 3 congruent pyramids. From this and a bit more it follows that the volume of any pyramid is (1/3) * base area * height.

• Symmetries of tetrahedra, cubes and octahedra
• Tetrahedron in the cube. Volume is 1/3 of cube.
• Octahedron in a tetrahedron. Volume of octahedron = 4 * volume of tetrahedron with same edge length.
• This implies dihedral angles are supplementary.
• Octahedron = 4 congruent pyramids with equilateral triangle bases and height = regular tetrahedron
• Octahedron in cube has vertices at center of cube faces.
• Cube puzzles show decomposition of cube into pieces related to the relationships above.

Links that show these polyhedral relationships

• Polyhedra 1.0 animates polyhedra in other polyhedra
• Ray-traced RealisticModels

Wednesday 11/27 487 Lab

• Lab 9 can be on done on your own or Zach will help you get started at the regular lab time.
• Lab Report 9 is due Wednesday, 12/4. The report questions are alsoin the text of the lab. (The report text is in red.)

Friday 11/29 444

THANKSGIVING HOLIDAY