- Your exams are returned.
- There is a curve: add 9 to your score.
- So you calculate your percentage by (score+9)/.90
- There is a key.
- Some students on the very low end of the distribution should drop;
others may recover. IF you believe that you can get this stuff, in time
for the final, then you might try to shoot for redemption. The
final will come in two parts: old stuff and new stuff. If you can do
better on the "old stuff" portion of the exam than this test (and you
must also do well on the next exam), then you might be okay.
So you have to ask yourself, without deluding yourself: am I going to be able to do this stuff 9 weeks from now, when I couldn't do it on this exam? If you can honestly answer "Yes.", then you might consider staying. Otherwise, you should probably exit gracefully...
- Do you have questions about the exam?
- Reading for next time: Keith Devlin examines Fibonacci and Golden Ratio mania
- Now let's retreat to 13th century Italy for a moment: the bunnies of Leonardo Pisano Fibonacci
- Start with a new-born pair of "immortal" bunnies (they never die).
- A new-born pair requires a month to mature.
- The following month, the pair produces a new pair, which is subject to the same rules.
- Do it again, do it again, do it again!
- Fibonacci number decomposition and Fibonacci Nim.
- If you looked at some special cases, what can we
conclude?
Number of sticks 1 2 3 4 5 6 7 8 Winner X - What's the winning strategy in Fibonacci Nim?
- If you looked at some special cases, what can we
conclude?
- The Fibonacci numbers as a recurrence relation
(do it again, do it again, do it again!). - More
details on Fibonacci numbers and nim. It turns out that
Every natural number is either
- Fibonacci, or
- can be written as a sum of non-consecutive Fibonacci's in a unique way.
Examples?
- Fibonacci
Numbers and Nature:
- Let's look at some pine cones....
- dandelions (Here's a scanned dandelion)
- Spirals in daisies:
- Similar things happen in artichokes, pineapples, etc.
- As we move toward the so-called "golden mean" and "golden rectangle", we'll start with a nice logarithmic spiral (see this site)
