While in the public library I was scanning the shelves of new release nonfiction DVDs and came upon a PBS NOVA episode that I'd never heard of called Fractals Hunting The Hidden Dimension. I borrowed it.
My two sons aged twelve and nine watched it with me yesterday. I found the show to be fascinating. As a non-mathematical person I found the show engaging and completely understandable. The show was not that dumbed down as while watching it, it was apparent that some of it was going over the head of my nine year old.
Fractal geometry is a different geometry than classic or plane geometry. Fractal geometry is applied to three dimensional objects.
One thing I loved about the content and production of the show is that at first it seemed very abstract and possibly unimportant to the layperson's life, but the show clearly showed how fractal geometry is relevant to modern living and has applications in the real world. When they explained that fractal geometry principals were used to create a new cell phone antannae that makes them more usable for customers around the world it was very clear that knowledge of fractals is important to daily life. It was said that engineers can use this new information in daily applications.
Another story of interest was that the tallest tree in a rainforest was studied. Measurements were taken of its trunk and branches and the fractal geometry calculations were in alignment. Of further interest was the same mathematical computation matched the design of the whole rainforest, the spread of the other trees, the smaller trees, the width and size of the forest was all in alignment with this. The scientists also gathered samples from the leaves to check CO2 content and the point was to calculate the effect of the rainforest had in relation to global warming.
It was also interesting when it was explained that when Benoit Mendelbrot, the mathematician who created formulas for fractal geometry shared his thoughts there were many people who doubted him and the entire theory.
Another cool thing was it was said that for thousands of years artists and architects have used principals of balance and eye-pleasing proportion inspired by nature, and that nature's designs matched the mathematical computation. Thus some artist's work that looks pleasing to the eye actually is in alignment with that mathematical operation also (without one ever having been done). This was brought full circle by showing a story of a textile design artist who used the fractal geometry formulas to create patterns for fabrics to use to make colorful printed men's shirts (similar to Hawaiian shirts).
My twelve year old son says he can't stop thinking about fractals now. He loves the idea and wants to learn more. He has asked me to get the book by Benoit Mandelbrot for him to read. I fear it will be too far above his head.
I'm looking for books at about a seventh grade (or high school) reading level about fractal geometry. If you know of one that you've used, can you let me know by leaving me a comment on my blog? I thank you in advance.
Meanwhile if you are interested in this show, it has great graphics that looked fantastic on my TV screen. If you can't get your hands on a DVD copy, such as from your public library, you can watch it free over the Internet on this PBS webpage (it's divided into parts).
An unanswered question is if fractal geometry is accepted into the field of mathematics now I wonder if it is being taught in public high school, or if they are 'lagging behind' the latest educational concepts and still only teaching the old plane geometry?
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