- You have a homework due today.
- We have our second exam Thursday, next week. Get ready! Tuesday of next week we'll do a review.
Remember that you can use your set of paper Platonic solids as a cheat sheet for the exam, but you must build them. And you can't share with a neighbor -- you have to build your own.
Question of the Day:
- Start with a piece of graph paper (the wide way), and darken the square in the 10,10 spot (ten over, ten down)
- Rule: attach the largest square you can, in either a clockwise or counter-clockwise fashion, to make a larger rectangle.
- Do it again, do it again, do it again! You could do it forever....
- What are the limiting dimensions of the rectangle? (We can use Excel again to help us.)
- The thing we are approaching is the golden rectangle. But we will derive the golden rectangle in a different way -- the way that the Greeks did it!
- Begin with a rectangle.
- Remove the largest square possible from the rectangle, to leave a rectangle.
- If the rectangle that results has the same shape as the original rectangle, then that rectangle is golden.
Now if we look back at the Fibonacci spiral sequence of rectangles, we see that they're tending toward a golden rectangle.
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!
Let's make one using 4x6 index cards.
- Use symmetry!
- How far off golden are we?
- Do you see the icosahedron?
You'll be able to use this object as a cheat sheet for the final exam.
