A few years ago I bought the toy zometool. I bought a lot of different pieces from different collections and now I have more than I’ll ever need. Zometool is really cool because it lets you build things without worrying about “forcing” things to fit. If a piece fits where you want it, then it fits exactly.

A shape

Put together without a plan

This construction was just put together by me picking a few struts and then extending them until they could close back on themselves. This is a hint at the wide variety of shapes zometool lets you create-the opportunity to be creative is endless.

A bunch of nodes

A bunch of nodes

The nodes that the struts are attached have 3 shapes of holes. Triangular that take yellow struts, rectangular that take blue struts and pentagonal that take red struts.

To me the math behind the design of the nodes and the lengths of the struts is very cool. Each color of strut comes in 3 lengths. The ratio between the lengths is the golden ratio (\phi).

One of the properties of the golden ratio is that \phi^ 2 = \phi + 1.

So, if I have one piece that is the golden ratio longer than the second, I have a strut with length 1 and \phi. The next longer strut would be \phi \cdot \phi = \phi + 1. That means if I want the equivalent of the next longer strut, I just need to add one of each of the two lower lengths.

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