Math 119: Ideas in Geometry
Spring 2008

Instructor: Tom Cooney


Classroom: 141 Altgeld

Time: 12:00-12:50pm Monday, Wednesday, Friday

Office: 150 Altgeld

Office Hours: 2:00-2:50pm Monday, Wednesday, Friday or by appointment.

Math 119 is a general education course in mathematics for students who do not have mathematics as a central part of their studies. The goal is to convey the spirit of mathematical thinking through topics chosen mainly from geometry.

Homework assignments, exam dates and other course details will be posted on this website. Here is the syllabus. You can check your grades at the compass website.
This course adheres strictly to the University's Student Code Part 4 Policy on Academic Integrity. Cheating of any kind on the homeworks, exams, or the final will result in a letter being placed in your permanent school file. A single very minor instance of cheating will be punished by a 0 on that exam, etc.. More serious offences or a second offence will result in an immediate F in the course. Any such student should feel free to continue attending the course and to continue learning (if they are not being disruptive) but their grade in the course will be an F. I would also like to add that any disruptive behaviour during any exams will result in a 0 on that exam and the student being asked to leave. If appropriate, more severe penalties will be imposed.

Take Home Exam Queries

Problem 1: What is the idea behind constructible numbers? We start with the length 1 and we build our way step by step towards more complicated numbers. We have constructions for addition, subtraction, multiplication, division and square roots. Can you construct the numerator? Can you construct the denominator?

Problem 2: Can you construct the circumcenter? Draw a rough sketch of a triangle (including circumcenter and circumcircle) and mark off all distances and special features you can.

Problem 3: Have we seen how to use these pieces of information before? Have we seen an example of how to use an opposite angle? Is there anything related to this in the notes? (Hint: p.120)

Homework 4 Due Date: Monday, the 21st of April

Hour Exam 4: Friday, the 25th of April

Take Home Exam: Handed out with Exam 4. Due next class (Monday, 28th of April). No collaboration!

Final Exam: Thursday, 8th of May, 8.00am to 11.00am

Here is a pdf file that shows (in glorious technicolour) how we can do the problem we ended with on Friday, 18th of April. Opposite Angle and Median Problem .

Homework Assignments

Homework Assignment 1

Section 1.1: Problem 7.
Section 1.2: Problems 6, 21, 36, 46.
Section 1.3: Problems 10, 18, 20, 26, 29.
Due Date: Monday, the 4th of February.

Homework Assignment 2

Section 2.1: Problems 14, 18.
Section 2.2: Problems 2, 8, 18, 22, 27, 32, 38, 43.
Due Date: Monday, the 25th of February.

Homework Assignment 3

Section 3.1: Problems 13, 17
Section 3.2: Problems 5, 8, 10
Section 3.3: Problems 4, 6
Section 3.4: Problems 2, 22, 33
Due Date: Wednesday, the 26th of March.

Homework Assignment 4

Section 4.1: Problem 15 (What is the radius?)
Section 4.2: Problems 7, 8, 24, 26 (Use the information from this file .)
Section 4.3: Problems 3, 10, 14, 33
Section 4.4: Problem 4.4 (Note: using compass and straightedge only)
Due Date: Monday, the 21st of April

Very Tentative Exam Dates

You will be given a week's notice of the actual exam dates. The hour exams will be held (in class) near the following dates:

  • Hour Exam 1: Friday, 8th of February. This exam will cover Chapter 1.
  • Hour Exam 2: Friday, 29th of February. This exam will cover Chapter 2.
  • Hour Exam 3: Monday, 31st of March. This exam will cover Chapter 3.
  • Hour Exam 4: Friday, 25th of April.This exam will cover Chapter 4.
  • Also,
  • Take Home Exam: Handed out on Friday, 25th of April. Due in class at 12 noon on Monday, 28th of April.
  • The final will definitely be held:
  • 8:00-11:00 AM on Thursday, May 8th 2008. The final will cover the entire course.
  • Students should bring their compass and straightedge to Hour Exam 4 and to the Final Exam.


  • Math 119 Webpage with online course notes
  • Tom Cooney's homepage
  • Course Webpage for Math 119 in Fall 2007
  • Monty Hall Problem Story from The New York Times
  • All possible regular (semiregular, demiregular) tessellations - very pretty!
  • Penrose tiling - tiles the plane, never repeats!
  • What is a tessellation?
  • Totally Tessellated
  • The Euclidean Toolbox An online tool to help you with compass and straightedge constructions. If you are in one of the University's computer labs, it should have at least one of the following: (The Geometer's) Sketchpad, Dr Geo. All very interesting and all with the potential to be very helpful.
  • Wikipedia A good source for interesting and often also true mathematical tidbits. Try searching for biographies of the mathematicians listed below.
  • Euclid, Erastothenes, Pythagoras, Heron, Brahmagupta, Descartes, Newton, Euler
  • Lots of mathematical info from Wolfram Research , one of the world leaders in mathematical computer software, based right here in Urbana-Champaign.
  • Euclid's Elements: The book(s) that helped start it all.
  • The MacTutor History of Mathematics archive : Mathematicians' biographies and more!
  • The Most Pleasing Rectangle Web Poll Poke around the rest of Jim Loy's webpage for some more interesting stuff.
  • Demetri Martin (a stand-up comedian) corrects the Rock, Paper, Scissors game (among other things).
  • The Geometric Meaning of the Geometric Mean Plenty of pictures showing the geometric mean in action.
  • When would you use the Geometric Mean? Average rate of return on investments, averages of things that fluctuate (the stock market for example), center frequencies, averages of things that you are multiplying by.
  • Some examples of the golden ratio in nature The numbers that appear (the Fibonacci numbers) are VERY closely related to the golden ratio. For example, 55/34 and 89/55 (and so on for the other numbers that appear on this webpage) are very close to the golden ratio.

  • Department of Mathematics
    College of Liberal Arts and Sciences
    University of Illinois at Urbana-Champaign
    273 Altgeld Hall, MC-382
    1409 W. Green Street, Urbana, IL 61801 USA
    Department Main Office Telephone: (217) 333-3350 Fax (217) 333-9576