- Your tests are returned
and there will be a key.
- Curve: add 6 to your score for your curved grade on exam 2.
- This is what was covered on your exam:
- Bases
- Translating between bases
- Doing addition/subtraction in bases other than 10
- Fibonacci numbers
- Rabbits
- Nim
- Spirals
- Golden rectangles
- Pascal's triangle
- Bases
- Midterm grades are posted (for freshmen). If you're
getting an F, you probably want to drop.
- You have a new reading assignment: Graphs, Idea 29, p. 116.
- Question of the day: What does the golden rectangle have to do with Platonic solids?
- Before the exam 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.
- Links:
- Links are like chains: constructed by "linking" loops (or
rings) together, into a necklace holder, say.
- Borromean
Rings: "Is it possible to create a link of three loops (or
rings) in such a manner that
they are indeed linked, yet if we
remove any one of the rings the other
two become unlinked?"
- Yes, indeed! Let's try it with rubber bands first.
Standard diagram of the Borromean rings
A realization of the Borromean rings as ellipses
Coat of arms (of the municipality of Hallsberg, Sweden) showing padlocks in Borromean rings configuration
(Thanks Wikipedia!) - icosahedra, golden rectangles, and
interlocking rings. It turns out that there
are golden rectangles in the heart of an
icosahedron
- Use symmetry!
- How far off golden are we?
- Do you see the icosahedron?
- Links are like chains: constructed by "linking" loops (or
rings) together, into a necklace holder, say.
