Tuesday, February 19, 2013

Precalculus Fractals

We are deep in our unit on complex numbers, and last class we talked about the 3 defining properties of a fractal and made the Sierpinski Triangle. Their homework was to find cool facts about fractals, and they came through. Today we watched some cool "zooming in" videos of the Mandelbrot Set and the Julia Set. Then we got to the business of understanding them by hand calculations (and the TI-84).

I don't know how much sunk in to how many people, but I hope I got across the insanity of 2 values REALLY close together on the complex plane can have wildly different results when applying the Mandelbrot Set iteration process. We also talked about how the colors come about.

Anyhow, bla bla bla, here was/is their homework, and I can't wait to see what they come up with for their own fractal. Most of this sheet is middle school level, but I figured it would drive home the iteration fact and the first few problems would give them an idea on how to create their own fractal. Maybe I should have incorporated complex numbers into it somehow. Next time? SHEET:

1 comment:

  1. Hi, Shireen,

    I came across your blog via David Wees, and as a fellow mathematics educator I thought you might be able to help in spreading the word about an educational TV show for preteens about math that we're putting together. "The Number Hunter" is a cross between Bill Nye The Science Guy and The Crocodile Hunter -- bringing math to children in an innovative, adventurous way. I’d really appreciate your help in getting the word out about the project.


    I studied math education at Jacksonville University and the University of Florida. It became clear to me during my studies why we’re failing at teaching kids math. We're teaching it all wrong! Bill Nye taught kids that science is FUN. He showed them the EXPLOSIONS first and then the kids went to school to learn WHY things exploded. Kids learn about dinosaurs and amoeba and weird ocean life to make them go “wow”. But what about math? You probably remember the dreaded worksheets. Ugh.

    I’m sure you know math is much more exciting than people think. Fractal Geometry was used to create “Star Wars” backdrops, binary code was invented in Africa, The Great Pyramids and The Mona Lisa, wouldn’t exist without geometry.
    Our concept is to create an exciting, web-based TV show that’s both fun and educational.

    If you could consider posting about the project on your blog, I’d very much appreciate it. Also, if you'd be interested in link exchanging (either on The Number Hunter site, which is in development, or on StatisticsHowTo.com which is a well-established site with 300,000 page views a month) please shoot me an email. We're also always looking for input and ideas from other math educators!

    Thanks in advance for your help,