- New Homework:
Wed 3/3 Finish Money Math; Start Fractals - Read the section on Chaos, p. 104
- Using the funhouse mirrors for fun (but no profit;): make your own funhouse mirror image, using my web interface and your own image, and I'll post them on our website "Mirrors gallery".
- Please give me a one-page, polished version of your updated project proposal (hand in next time, 3/17).
- Upcoming talks and events:
- For those going to the KYMAA meetings, March 26/27: Registration form (fill out and give it to Suzanne, or me! Make sure that you sign up for the Friday night banquet)
- No Friday's seminar this week (Spring Break is coming up, of course!).
- Reminder: http://prime.nku.edu/ scholarships are still available: please encourage any qualified current freshmen or incoming freshmen to apply.
- How
do the credit card companies make so much money?
- How do
mortgages work?
- Other loans can be calculated the same way: for example, CitiFinancial's loan shark fishing attempt on me.
- You encounter a few laws such as The rule of 72 (70, 71,
69.3,...) to calculate doubling time: forget them! Just do the
math: we want to find out how long until
That is, until
where n is the number of compoundings per year, and r is given as a decimal (e.g. 9% is represented by .09).
When compounding is continuous (i.e.
), this reduces to the very lovely rule for the doubling time:
- It's a graph that possesses "self-similarity".
- It often possesses a simple and recursive (or iterative) definition.
- Deterministic
fractals: delve into an infinite, dynamic world, created by
a simple mathematical process:
- a simple rule
- repeated over and over and over.... but
- simple rules, intense content!
- Let's
see the process works with sticks (check out the
beautiful bushes...).
- The Sierpinski triangle:
- First deterministically: fractals by subtraction
- After we're finished removing all that stuff, how much area is left in the triangle?
- Now let's introduce a little bit of randomness:
| Here's our mascot for this unit: Bessie the fractal cow: |
|
| We might have easily taken the Japanese artist Hokusai. |
So what is a fractal? A couple of things we'll generally see: