Friday, August 22, 2008
Monday, August 18, 2008
Tuesday, August 12, 2008
Fibonacci numbers and the golden ratio are abundant in nature. In fact, I noticed the ratio while admiring a dragonfly. I went to work and eventually built one out of Zomes.
I actually needed a few extra small struts--these, too, maintain the golden ratio in relation to the other struts. I didn't have enough struts to make the second wing.
The website and kits have a wide range of geometric models, from simple Platonic solids to a complex taurus (doughnut) and even a large DNA model. You can download a set of challenge cards, or lesson plans for grades 1 through 12.
This makes a great math and science manipulative especially if your kids like to build like my boys do. Their imaginations are their guides!
Saturday, August 2, 2008
An excellent example of the intertwined existence of Science, Math, and Nature are Fibonacci numbers and the Golden Ratio. And yes, there's Art, too.
The Fibonacci sequence is easy to construct. Starting with 1 (one) and 1 (one), you add the previous two numbers to get the next in the sequence. 1, 1, 2 (from 1 + 1), 3 (from 1 + 2), 5 (from 2 + 3), 8 (from 3 + 5) and so on.
You can then construct a spiral by creating squares with each side the length of a Fibonacci number and put them together such that they go around in a circle, as in the picture to the left. See the two 1x1 squares stacked one on the other in the center? There's a 2x2 box attached to the left of those, a 3x3 box below that, a 5x5 box to the right of that, an 8x8 box above that, and so on. Using a curved line through each box, a spiral is created.
It turns out that these numbers and spirals occur frequently in nature. A nautilus shell and flower seed head exactly spiral in this way. The number of petals on a flower are almost always a Fibonacci number. Wild Fibonacci by Joy Hulme is a wonderful introduction to this connection for young readers.
Also notice that with the addition of each new square, the final drawing forms a rectangle. The ratio of the long side to the short side in this rectangle (which is the ratio of two consecutive Fibonacci numbers, a Fibonacci number and the number before it in the sequence) is the Golden Ratio, or Φ (Phi) and equals 1.618. O.K., enough math.
Besides appearing so much in Nature, this rectangle seems to be appealing to people, too, for we often use it in our art. Check out Fibonacci Numbers and Nature and Fibonacci Numbers and The Golden Section in Art, Architecture, and Music, both full of more details, pictures, links, and fun activities.
This is a great way to combine Nature Study, Math, and Art Appreciation.