444 Home Page

1. Week 10/01-05

2. Week 10/08-12

3. Week 10/15-19

4. Week 10/22-26

5. Week 10/29-11/2

6. Week 11/05-09

7. Week 11/12-16

8. Week 11/19-23

9. Week 11/26-30

10. Week 12/03-07

11. Week 12/10-14

Monday 12/10 444

• Assignment Due. Patterns of Centers. Kites and Circles. Dissections from Tessellations.
• Further links to dissections.

In class, two theorems were proved using transformations

• Napoleon's Theorem states that if A', B', C' of are the centers of 3 equilateral triangles built (externally) on the sides of any triangle ABC, then triangle A'B'C' is equilateral triangle. (The center of A'B'C' is the centroid of ABC, contrary to what I said in class in response to a question.).
• The Fermat Point of a triangle ABC is the point F such that the lines AF, BF, CF form angles of 60 and 120 degrees (i.e., these 3 lines have a 120-degree rotational symmetry. This point can be constructed as the intersection of segments from a triangle vertex to the vertex of an equilateral triangle on the opposite side. (Comment: F is the point P that minimizes the sum of the distances |AP| + |BP| +|CP|.)

Here is a page of links for Napoleon and Fermat that tell you more than you want to know about them.

Wednesday 12/12 444

This page shows what is called the p6 pattern generated by two rotations by 60 degrees. One tool for combining transformations is called conjugation.

In class some theorems about chords, secants, tangents and angles were discussed.

Wednesday 12/12 487

Lab: Some new and old circle constructions and constructions of isometries. Also, some miscellaneous problems.

Friday 12/14 444

Final Exam!

Links to Study Resources

Link to Final Exam (pdf format, requires Acrobat Reader)