Agenda

1. Quiz (5 min.)
2. Questions/discussion (5 min.)
3. Review (5 min.)
   • plane figure; configuration of points in the plane
   • similarity
   • Comments on measuring, length and ratio
4. Thales Theorem and its converse (30 min.)
   • Euclid VI:2
   • Proof. Role of Euclid I:35. Parallelism. Stillwell, p. 34-5.
   • Meaning of "converse", "contrapositive" and "obverse". Converse of Thales. Handout.
   • Stillwell 1.4.2 (page 12).
5. Theorem of Pappus (Stilwell 1.4.3.) (10 min.)
6. Theorem of Desargues (Stillewll 1.4.4.)
7. The Sea Island Problem. (25 min.)

Homework

• Complete by 02/06/06: Read Stillwell, Chapter 2.
• Hand in 02/08/06: Stillwell 1.3.6, 1.4.1, 1.4.2, 1.4.3, 1.4.4, and the problems on the Sea Island Page here.

Post-class report on what we did.

• Agenda items 1--5 were completed
• A test on February 22 was announced.
• Other stuff
  • Propositional logic
    1. An implication P is equivalent to its contrapositive:
       • P: If A then B. (If X is from Dublin, then X is from Ireland.)
       • Contrapositive of P: If not B then not A. (If X is not from Ireland, then X is not from Dublin.)
    2. P is NOT equivalent to its converse
    • Converse of P: If B then A. (If X is from Ireland, then X is from Dublin.)
    3. The contrapositive of the converse is sometimes called the inverse:
       • Inverse of P: If not A then not B. (If X is not from Dublin, then X is not from Ireland
  • Conversion of Ratios. Suppose A, B, C and D are magnitudes. If any one of the following is true, then so are all the others:
    • A/B = C/D
    • B/A = D/C
    • A/C = B/D
    • (A+C)/C = (B+D)/D
    • A*D = B*C