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!

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