Creating a method for spiral study

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Creating a method for spiral study

Postby Niki » Thu Jan 06, 2011 7:11 am

My daughter is entering her first science fair and is interested in the Fibonacci sequence and the golden mean. She really likes the way spirals show up in nature. We came to this subject via multiplication studies-math is the science of patterns. This web sight is one of her reference (page 11)
http://spigotsciencemag.com/site/spigot-issues/patterns
Her question is: If there are patterns in math are there patterns in nature?
Her hypothesis is:""Yes there are pattens in nature because she has seen them in pinecones, sunflowers, artichokes.
I'm concerned we are being too broad and need some help guiding her to a focused topic. She likes the patterns in sunflowers, pinecones, pineapples, artichokes, broccoli romanesco and brussels sprouts. So we thought she should focus on spirals.
After collecting samples, taking pictures and coloring them to show the spirals, we need to create a method for her to duplicated them by herself using the Fibonacci numbers.
Any suggestions for a 3rd grader to do this for each the different samples she is planning on using?
Also, is this a math topic or a botany topic?

Thank-you,
Niki
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Re: Creating a method for spiral study

Postby dcnick96 » Sat Jan 08, 2011 7:58 pm

Hi Niki:

I love this topic. Fibonacci sequence in nature is so exciting and definitely makes you look at things like flower petals and shells in a different light. I definitely agree that you should narrow your topic. If she likes spirals, perhaps she can concentrate on shells. Nautilus shells, in particular, are a perfect example of this phenomenon, and I think it is doable at the elementary school level.

Your hypothesis is fine: There are patterns in nature.

To test this, follow the steps on this website to draw a spiral using the Fibonacci sequence, and show how this exists from a picture of a nautilus shell. A simple way to draw the boxes would be to use graph paper, so that smaller boxes are already drawn. The existing squares can be called a size of one, and you can combine these together to make your sizes of 3, 5, etc. (This should make more sense after you view the website).
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html#golden

Good luck to your daughter in the science fair. Be sure to write back if you have any more questions!
Deana
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