What are other ways to represent a 3d shape in two dimensions?  We saw last class that you can use one of several different views, but we can also take the shape and look at its "skin".  When you cut a polyhedron along some of its edges to lay it flat, we get a net:

Resources:

• Notes: 5.2 Nets
• Triangular Prism
• Rectangular Prism

Fun Ideas with Nets and Networks

• Polyhedron Nets (paper nets)
• Konigsberg Network Problems - read about Euler's solution to the "bridge" problem and about 4 colour map theory!
• Six Degrees of Separation  Network theory was the foundation for the idea that every person in the world is connected by no more than 6 connections.  This was popularized in the game "Six Degrees of Kevin Bacon" that appeared in the early 1990's.  While designed to be a trivia game, the Oracle of Bacon will quickly find any actor's "Bacon Number" for you.

Pre-Class Assignment:

• Before next class, read through the notes and copy them down into your notebook.
• Think about the following 2 questions:
  • Do you think a net is more or less effective at representing a 3d shape two dimensionally than the 3 views?
  • Is there a way to figure out how many faces, vertices and edges a shape will have by looking at its net?  Use the examples of the triangular prism and the rectangular prism to help you.

In-Class Assignment:

• P173 #3, 4, 6, 7, 8, 9, *12 *13
• Koninsberg Network Problem