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Syllabus

Homework assignments:
Note that late HW is not accepted!

Monthly HW assignments (collected):
HWI: 1.1(3),1.2(2,4: Stewart's Thm used frequently later; use law of cosines to prove),1.3(2,5), 1.4(2,3),1.6(1).
HWII: 1.7(4),1.8(3), 2.1 (4,8; for 4 you should first solve 3 but only turn in 4), 2.2 (1,5), 2.4 (1,2), 2.5 (4).
HWIII: 2.6 (2), 2.7 (1), 2.8 (1), 2.9 (1,3), 3.1 (2,3 hint: recall Stewart's thm), 3.2 (5,10), 3.3 (3).

Weekly HW assignments (not collected):

Wk 2 (ends Fr 9/5) (Mon 9/1 Labor Day): 1.2(3), 1,3 (1,9).

Wk 3 (ends Fr 9/12): *During Monday's review we showed that if a segment BC is seen from A and D at the same angle, then ABCD is cyclic. We only proved one case. Complete the proof by proving the second case.
*Is Lemma 1.511 still valid if the angles are obtuse (this was raised by a student during class). 1.4 (1,4), 1.6 (3).

Wk 4 (ends Fr 9/19): (HW I due on Wed 9/17) 1.7 (3).

Wk 5 (ends Fr 9/26): Show that the circumcenter of a right-angled triangle lies on the hypothenuse, and determine where exactly. Use this result to construct (using only compass and ruler) the tangent line from a given point P to a given circle. (Ex I on Fr 9/26; review on Wed 9/24).

Wk 6 (ends Fr 10/3): 1.8(1,2,5) Verify that Theorem 1.91 remains valid if P is outside triangle ABC but not on its circumcircle, 2.1(1,2,3, and 5 which we already did in class).

Wk 7 (ends Fr 10/10): 2.2 (2 (use 2.1#3),4), 2.3 (2, use 2.1#3).

Wk 8 (ends Fr 10/17): 2.5 (2,3), 2.7 (2).

Wk 9 (ends Fr 10/24) (Fr 10/24 Homecoming, HW II due on Wed 10/22): 2.6 (1), 2.8 (2, hint: draw line AT and find intersection Q with extension of PB).

Wk 10 (ends Fr 10/31): no HW(Ex II on Fr 10/31; review on Wed 10/29).

Wk 11 (ends Fr 11/7): 2.9(2,5), 3.1 (1, verify proof of Ceva's Thm and its converse when some Cevians meet the EXTENSIONS of the sides of the triangle; verify proof of Varignon's Thm for a re-entrant quadrangle).

Wk 12 (ends Fr 11/14) (Tue 11/11 Veterans Day ): 3.1 (4), 3.2 (1,5,9; hint for 5: recall ex 1.1#3).

Wk 13 (ends Fr 11/21): 3.3 (1,2).

Wk 14 (ends Fr 11/28) (Th-Fr 11/27-28 Thanksgiving): presentation preparation (no other HW).

Wk 15 (ends Fr 12/5): (HW III due on Wed 12/3, review for Ex III on Fr 12/5): presentation preparation (no other HW).

Wk 16 (ends Fr 12/12): (Ex III on Wed 12/10).

Announcements:

A comprehensive and quite interesting site with many theorems and their proofs and nice applets can be found here. For the class presentations I will assign theorems from this site.
Another interesting resource is Gerard A. Venema's Exploring Advanced Euclidean Geometry.
Exam I covers what we saw in class on sections 1.1-1.6, plus any review material that we discussed. For the format of this exam, see the syllabus.
Solution to last problem of exam1: Let AB=AC=2 and BC=sqrt(3). Then in triangle ABC the angle at B is determined by cos(B)=sqrt(3)/2, and thus B=30 degrees. The incenter I is the intersection of the angle bisector of B and the altitude from A to BC (this altitude is also the bisector of angle A because triangle ABC is isosceles). We need the distance from I to the foot X of the altitude from A to BC. Since triangle BIX has a right angle at X, and the angle at B is 15 degrees (half of 30 degrees) it follows that the inradius is determined by: tan(15)=r/sqrt(3), and thus r=sqrt(3)tan(15).
Exam II covers what we've seen in class on sections 1.7, 1.8 and 1.9 and of sections 2.1 up to and including 2.5. The format is the same as that of Exam I.
Exam III covers what we've seen in class on sections 2.6, 2.7, 2.8 and 2.9 and of sections 3.1 up to and including 3.3. The format is the same as that of Exam I.
Solutions to some problems I promised to post when we were having our Review II (of Wed, Oct 29, 2008).
Solution to some problems of Exam II.
Class on Mon 12/8 is canceled.
List of class presentations: First come first serve basis (email me if you made your choice, and I will put your name next to your pick in the list below). (1p) is a 1 person presentation, and (2p) a 2 person presentation.
1. The broken chord theorem (1p) Stephen
2. Hiroshi Haruki's Lemma (2p) Erin and Jennifer
3. Fagnano's problem (1p): see section 4.5 in text on p 88.
4. The diagonal of a regular pentagon with side 1 has length equal to the golden ratio (don't use trig) (1p) Joanne
5. Thm 1.92: The third pedal triangle is similar to the original triangle (see section 9 in chapter 1 of our text) (1p) Diana
6. Haruki's Theorem (1p) Chan
7. Approximate construction of regular pentagon by Albrecht Durer (2p, one person shows the construction, the other person shows it is an approximation; extra credit if you tell us more about Durer) Mallory
8. Thebault's Problem I (1p) Note: do proof 1, but you will need to clean it up first: the way it is written now is too sloppy. Ben
9. Nagel Point (1p or 2p) Shira
10. Nagel point of medial triangle (1p) Kyle
11. The Eyeball Theorem (1p) (Proof 2) Amanda
12. The Squinting Eyes Theorem (1p) The proof given is too colloquial, and needs improvement. If you wish to do this project, see me first, so we can discuss a better proof.
13. Copernicus' Theorem (1p) Eric
14. Circles and Semi-circles in a rectangle (1p) Chad
15. Peacock's Tail Sangaku (1p) Rachel
16. A median in touching circles (1or 2p)
17. 60 degrees breeds 90 degrees (1p) Corey