15-344/Homework Assignment 6

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This assignment is due at the tutorials on Thursday November 12. Here and everywhere, neatness counts!! You may be brilliant and you may mean just the right things, but if the teaching assistants will be having hard time deciphering your work they will give up and assume it is wrong.

Reread sections 5.1-5.4 of our textbook. Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. Also, preread sections 5.5 and 6.1, just to get a feel for the future.

Solve problems 4, 8, 18, 39, 46, and 49 in section 5.1, problems 4, 9, 16, 23, 31, 38, 56, 68, 72, and 85 in section 5.2, and problems 5, and 29 in section 5.3, but submit only your solutions of the underlined problems.

Sorry for again posting an assignment a bit late.


An unrelated matter - I was asked to distribute the following, and I hereby comply:

Subject: COMC Markers Needed

We need people to help us mark the 2015 Canadian Open Mathematics Contest. Anyone can help mark (including non-math students so please feel free to pass this message onto your friends and invite them to help too).

We are having a marking party on November 21 and 22 complete with pizza, pop and other snacks. However we need markers to help the week before and after this as well. Anyone who assists will gain hours towards CCR recognition and certificates are provided to those that wish them.

If you are able to help please send an email to outreach@math.toronto.edu with "COMC Marker" as the subject and we'll add your name to the list. We're also happy to answer any questions you may have.

Sincerely,

Pamela Brittain
Outreach and Special Projects Officer
Department of Mathematics
University of Toronto

Dror's notes above / Students' notes below

In Problem 85, Section 5.2, we were asked to find the number of triangles formed by pieces of diagonals or outside edges of an n-gon, assuming throughout that no three lines were collinear. What if there is no such constraint? Attached are two articles that presented some general results.

15-344/The Number of Triangles Formed by Intersecting Diagonals of a Regular Polygon

15-344/The Number of Intersection Points Made by the Diagonals of a Regular Polygon