Friday, August 22, 2008

Compound microscope update

I rechecked the prices and links for the post about buying a compound microscope, so if you are in the market for one or think you might be, I hope you find the guide helpful.

Monday, August 18, 2008

Yet Another Cool Interactive Periodic Table

The Visual Elements Periodic Table is a great interactive resource. Clicking on an element in opens another page with a quick "fact sheet" about that element. It lists the name, discoverer, the origin of the name, and some properties about each element. It makes a neat guessing game, too, since the element names are not listed on the table, only when you mouse over the element on the table.

Tuesday, August 12, 2008

More About the Golden Ratio: Zomes

The folks at Zometool have created a very sophisticated "toy" using Φ. Vaguely reminiscent of Tinker Toys, it is far more elegant and mathematically designed.

Basically, it consists of struts and nodes. In a basic set, the struts are blue rectangles (representing 2,) yellow triangles (representing 3), and red pentagons (representing 5.) 2, 3, and 5 are part of the Fibonacci sequence.

Each strut comes in 3 sizes--small, medium, and long--and guess what the ratio is among them? That's right, Φ. You can easily build golden rectangles with them like those overlaying the chameleon's tail in the previous post.

The struts connect to the nodes. These are white with carefully placed rectangular, triangular, and pentagonal holes such that structures can be built that demonstrate mathematical and geometric principles. That is what you see in the Zome logo.

They also have green line struts, which are advanced pentagon struts that have angled ends, that can build additional geometric structures. Here's the strut catalogue:

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

Math, Science, Art, and Fibonacci

Science, Math, and Nature are so closely related one can scarcely separate them. So while this is a science blog, and not a math blog, math will come up from time to time.

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.