Table of topics and assignments  

Learning Assistant for our class is Hector Leon. His (new) schedule: MW 1-2pm, TR 11am-12noon, outside (or inside) DM 409A.

You can also see me in my office TR 2:30-3:30pm.

Date Topics Covered Suggested Assignment Comments
Jan. 10 Review material
class exercises
 		For your review, here is an Appendix from a book by James Smart.
You should know all concepts and Theorems in there.
For further exercise, taking as axioms S25, S1, S2, S3,
S7, S8, S9, S16, S21, S24, from the Selected Theorems section, prove the other 
properties from these.
(You can rotate the file using right click; also, I hope you can identify S1, ... S10 - the copy did not come out well.)
Jan. 12 1.1 - Extended Law of Sines
1.2 - Ceva's Theorem		 1-4 + week1 class exercises
1-4		 In the box on the left, you have a link for all additional exercises
that I would suggest you would do for week 1.
Homework 1 - to hand in by Thursday, Jan. 19 -
(1) Prove S4 and S12 from the above appendix (taking as axioms any of the needed statements among S25, S1, S2, S3,
S7, S8, S9, S16, S21, S24).
(2) Prove #2 from the week1 class exercises on the left.
Jan. 17 3.4 - Menelaus Theorem see comments Use Menelaus Theorem twice to prove the direct implication of Ceva's Theorem
(if three cevians are concurrent, then the product of the ratios is 1).
Jan. 19 1.3- Important Points 1-9 Homework 2 - to hand in by Thursday, Jan. 26
Jan. 24 1.4- The incircle and the excircles 1-6  
Jan. 26 1.6- The orthic triangle
1.7- The Euler line		 1-4
1,2		  
Jan. 31 1.8 The nine-point circle 1-4  
Feb. 2 Review Chapter 1 1-3, page 25 Homework 3 - to hand in by Tuesday, Feb. 6
Pb. 7 page 11, textbook; Pb. 4 page 22, textbook.
You receive 2 bonus points if you do the second problem based
on the following  idea: show that triangle ABC is congruent with
the triangle formed by the centers of the three circles.
Feb. 7 Apollonius Circle
2.1. Power of a point w.r.t. a circle		 Suggested Pbs on Apollonius
1-8		 Exam 1 will be on Tuesday, Feb. 21 (postponed one week compared to syllabus).
It covers all sections done up to and including Feb. 14. You need to know well all the definitions
and the statements of the important theorems covered. Easy parts of the proofs of these
important theorems could be questions on your exam. Also any problem in the suggested or
assigned homework is a possible exam question.
Feb. 9 2.2. Radical axis of 2 circles
2.3 Coaxal circles		 1-4
1,2		 These are copies of exam 1 given in past years:
Exam 1 - Spring 2010 - you may ignore Pbs. 1(e), 2, 7.
Exam 1- Spring 2009 - you may ignore 8 (a).
Feb. 14 2.4 More on orthocenter (Thm 2.46) 1,2
  
Feb. 16 Review for Exam 1    
Feb. 21 Exam 1    
Feb. 23 1.9 Pedal triangles (just Thm. 1.91)
2.5 Simson lines
2.6 Ptolemey's Thm
1-4
1-3		 Homework 4 - to hand in by Thursday, March 1
Feb. 28 3.2 Brahmagupta's & Heron's Formulae 1-10  
Mar. 1 3.1 Varignon's Thm. & extensions 1-4 I recently discovered this link to a (free) book by Gerard Venema covering many of our class topics.
The emphasis is somewhat towards the software, but I think you'll find useful and interesting things in it.
Mar. 6 Menelaus & Ceva revisited
The extended Euclidean Plane
Pbs. 1-3 from the pdf file		 The lectures this week are related to Chapters 2 & 3 from
a geometry course taught at Cornell by Prof. Bob Connelly
Mar. 8 The axioms of Projective Geometry Pbs 1-6 from the pdf file Homework 5 - to hand in by Thursday, March 22
Pbs 3, 4, 5, 6 from the pdf file on the left (The axioms of Projective Geometry)
Have a good Spring Break!
At the bottom of page 2 of the file there is a typo:
points p_1, p_7, p_4 (not p_3) are on a line.
Mar. 20 Principle of Duality
3.5 Pappus Theorem		 Read 9.1 from the link on the left
1,2		  
Mar. 22 3.6 Desargues' Theorem 1-4  
Mar. 27 Isometries of Euclidean plane
 Isometries exercises The main result proved is: Any isometry of the Euclidean plane can be obtained as a composition
of at most 3 reflections.
Mar. 29 4.1 Translations 1,2 + more translation pbs
 Homework 6 - to hand in by Tuesday, April 17 - Pb. 1 from "Isometries exercises",
Pb. 1 from "more translations pbs" , Pb. 1 from "more rotations pbs"
Apr. 3 4.2 Rotations
4.3 Half-Turns
 1,2,3
1,2,3
 + more rotations pbs		  
Apr. 5 4.4 Reflections
4.5 Billiards and Fagnano Problem		 1,2,3
read the Fagnano Problem
  
Apr.10 4.7 Dilations 1,2 + suggested exercises Exam 2  is rescheduled to Tuesday, April 17.
It covers material done between Feb. 23 and April 10.
Apr. 12 Review for Exam 2  Know well all the definitions and the statements of the important theorems covered.
A good part of the exam will test just this. For the rest, you will likely get some
problems straight from those suggested ones and maybe one or two new ones. 		We'll start the exam at 9:00am so you will have some extra time.
Apr. 17 Exam 2 Here is a copy of Exam 2.
You may do Pbs 6,7,8 at home until Thursday, Apr. 19, and receive half of the credit
for at least two of them. Certainly this is valid only for the problems that you did not solve
or did not solve well on exam already. No extension beyond Apr. 19 for this offer!		 There were two unpleasant typos in my "more translation problems":
-- in Pb. 2 instead of M_2 on circle C_2, should be
N_1 on C_2.
--in Pb.4, instead of AB and CD should be AB and BC.
I now corrected the file. Sorry for the 12th hour corrections!
Apr. 19 Review for Final As with the other exams, a considerable part of the final will test your knowledge of the definitions
and important theorems covered in the course. Be sure to know them well. Review also the problems in your
previous exams and homeworks.		  
Apr. 24 Final Exam - 9:00-11:20
 - regular room		 Here are your scores. The last column is your grade for the class.
The bonus column are the bonus points you gained for Exam 2
("nn" means that you did not need the bonus).		 Have a good Summer!