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M4005 Geometry
February 1, 2006
Agenda
Quiz
(5 min.)
Questions/discussion (5 min.)
Review (5 min.)
plane figure; configuration of points in the plane
similarity
Comments on measuring, length and ratio
Thales Theorem and its converse (30 min.)
Euclid VI:2
Proof. Role of
Euclid I:35
. Parallelism. Stillwell, p. 345.
Meaning of "converse", "contrapositive" and "obverse". Converse of Thales.
Handout.
Stillwell 1.4.2 (page 12).
Theorem of Pappus
(Stilwell 1.4.3.)
(10 min.)
Theorem of Desargues
(Stillewll 1.4.4.)
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
.
Postclass report on what we did.
Agenda items 15 were completed
A test on February 22 was announced.
Other stuff
Propositional logic
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.)
P is NOT equivalent to its converse
Converse of P: If B then A. (If X is from Ireland, then X is from Dublin.)
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