M4005: Geometry
Spring 2004

Class Log

Record of classes and assignments.

Jan. 26 Triangle area continued. Lecture about the readings. See assignments at the topic page.
Jan. 28 Triangle area continued. Class discussion.
Feb. 2 Post-test on triangle area; see report. New topic: Parallelograms. Topic Page. Pretest. Introduction.
Feb. 4 Parallelograms continued. Discussion of definitions; see readings on definitions. Discussion of parallelogram theorems. HW: Write proofs of the equivalence of items i)-iv) I of the Parallelogram Theorem.
Feb. 9 Parallelograms continued. Review of some geometric contstructions with ruler and compass(approx. 50 minutes). Discussion of student work from last year (approx. 30 minutes). HW: Write final versions of your proofs of the Parallelogram Theorem. Extra credit: 1) Prove or disprove Roseanne's conjecture. 2) Prove or disprove John's Conjecture.
Feb. 11 Discussion of pre-/post tests, grading, teaching styles (20 minutes). Parallelograms continued. In groups of 3 to 6, students read, compared, discussed and revised proofs from their homework (40 minutes). Several proofs were put on the board, presented and discussed (15 minutes). HW: 1) Revise your proofs again, and submit on Monday. 2) Read Euclid Book I; see Euclid Topic Page.
Feb. 16

New Topic: Euclid. Pre-test: "What is a definition? A postulate? A theorem? What role do these things play in a logical deductive system?" (10 minutes).

Lecture Euclid, Book I, Propositions 1-26.

 1-3 various ways of reproducing line segments 4-8 triangles: (4) the SAS criterion for congruence, (5-6) properties of isosceles triangles, (7) the ASA criterion for congruence and (8) the SSS criterion for congruence 9-12 basic ruler and compass constructions: bisecting angles and segments and drawing a perpendicular to a given line through a given point 13-15 the angles formed when two lines meet, including the fact that vertical angles are congruent 16-21 inequalities between various parts of a triangle: (16) an exterior angle is greater than either of the opposite interior angles; (20) the total length of any two sides exceeds the length of the third 22-23 constructions of triangles 24-26 inequalities involving comparisons between two triangles and (26) the AAS criterion for congruence.

HW:1) Read all the propositions in Euclid Book I. 2) Continue the grouping, above, through Proposition 48. I want you to study the proofs until you understand them and can reproduce them in your own words and explain them to other people. (This will take many readings and a lot of work. I am asking for a lot, here.)

Feb. 18 Students turned in their work on parallelograms. Geometer's Sketch Pad. Students were introduced to GSP. Running it on laptops, they carried out the constructions in Euclid I.2 and I.16. HW: Continue assignment from 2/18.
Feb. 23 Lundi avant Mardi Gras
Feb. 25 Gueule de bois Mercredi
Mar. 1 Euclid Book I (continued). Continued the overview of the structure of Book I. Described the role of the Parallel Postulate. (See the commentary accompanying Proposition 29 in Joyce's web edition of Euclid.) Noted relations to specific topics and themes from the high school curriculum, e.g., "alternate interior angles", the parallelogram theorems, triangle area. Discussed the TIMSS video of the 8th-grade Japanese geometry lesson.
Mar. 3 Dr. C.N.Delzell discussed Euclid's proof of the Pythagorean Theorem, then led an activity from the book, 101 Great Ideas... by Posamentier and Hauptman illustrating how subtleties of definitions, if overlooked, can cause errors.
Mar. 8 Post-test on Parallelograms. Lecture: "How logically sound is Euclid?" Although Euclid was THE model of logical rigor for over two millennia, in the 19th century mathematicians realized that there were some subtle flaws in Euclid. What are these flaws? (Russell) Can they be fixed? What is the significance of this and the relevance to teaching high school? More discussion of definitions.
Mar. 10 Discussion and analysis of some student work (proofs).
Mar. 15 Test
Mar. 17 Activities related to ratio and proportion: TEXTEAMS "Perplexing Puzzle". Using a rubber band to dilate a figure. Lecture: Similarity of triangels, AAA criterion, measuring distant objects by triangulation. HW. Read the report by the Olberdings on activities they designed.
Mar. 22

Week 0: Jan. 21
Week 1: Jan. 26, Jan. 28
Week 2: Feb. 2, Feb. 4
Week 3: Feb 9, Feb. 11
Week 4: Feb 16, Feeb 18
Week 5: March1, March 3,
Week 6: March 8, March 10,
Week 7: March 15 (midterm test), March 17,
Week 8: March 22, March 24,
Week 9: March 29, March 31,
Week 10: April 12, April 14,
Week 11: April 19, April 21,
Week 12: April 26, April 28,
Week 13: May 3, May 5