Day 24, MAT115

Last Time

Next Time

Announcements:
- Your homework is returned.
  - Complete simple graphs:
    
    (6,1), (7,1), and (8,1) are the complete simple graphs with 6, 7, and 8 vertices. But how do we find the number of edges? Pascal's triangle! They're triangular numbers: $\frac{n(n-1)}{2}$
    How can we figure it out that they're triangular? Use symmetry.
  - All simple graphs with four vertices can be considered simple graphs on five vertices, as well. These are all subgraphs.
  - All simple graphs with five vertices, organized using the concept of duality.
- We have our second exam Thursday.
Question of the Day:

Will you be ready for the exam?
Last time we finished on a high note: the RCO -- Really Cool Object -- which brings together the borromean rings, golden rectangles, and an icosahedran. It turns out that there are golden rectangles in the heart of an icosahedron, interlocked as Borromean rings!

If you throw in the vertices at the corners, you can think of it as a simple graph as well. It's got everything in it!
Today we'll start with a review, based on your questions, and then I'll add a few remarks. If there is time remaining, we'll do some "supplementary activities" that illustrate some of the big ideas of the last several weeks.
The topics for the exam are:

Website maintained by Andy Long. Comments appreciated.