- Your homework
assignment was kind of rough: here's a key.
- Reminder: you will have an exam this Friday, the
21st.
- It will cover everything from bases to Pascal's triangle.
- It is not comprehensive, so it will not cover material from exam 1.
- Last time we created a set of Platonic solids in 3-d,
using a paper
template.
One of the advantages of making a nice set of these is that you will be able to use them, with anything you want written on them, for the exam. They
- must be constructed -- built! no flat versions -- from an 8.5"x11" piece of paper (just like the one I give you in class); and
- You can't undo them during the test.
- There will be a few questions over the reading. If you've done the readings, you should be in good shape.
- Question of the day: What does the golden rectangle have to do with Platonic solids?
- Review: let's start with the most recent homework, and then we'll
go all the way back to anything from
- Bases
- Translating between bases
- Doing addition/subtraction in bases other than 10
- Fibonacci numbers
- Rabbits
- Nim
- Spirals
- Golden rectangles
- Pascal's triangle
- Bases
- Last time we filled in the following table:
# of Vertices Edges Faces faces at each vertex sides at each face Tetrahedron 4 6 4 3 3 Cube 8 12 6 3 4 Octahedron 6 12 8 4 3 Dodecahedron 20 30 12 3 5 Icosahedron 12 30 20 5 3 What conclusions did we draw from this data? What's the pattern?
- Duality:
Each Platonic solid has a "twin" -- called its dual -- which we can discover from the table.
Let's make one using 4x6 index cards.
- Use symmetry!
- How far off golden are we?
- Do you see the icosahedron?