## Monday, November 23, 2009

### Net Result

I really enjoy designing nets (2-D plans that fold up into 3-D objects), and I love designing them in dynamic geometry, where you can design all nets. If I ever got the time to do math research again, I can see going in that direction.

I designed these four sketches for my geometry class, which is working on a project to design their own package with a few constraints. Each sketch is available as a dynamic webpage or the geogebra file. Here's 5 nets that were made with the sketches, in a printable pdf format. Geogebra actually has very nice priniting controls, so if you're interested in designing your own, choose that option. Remember you can install it, or run it from your browser at geogebra.org.

General tetrahedron: webpage or geogebra file

Square pyramid: webpage or geogebra file

Convex oblique pentagonal prism: webpage or geogebra file

I was very disappointed that the above sketch, though intuitive, couldn't make concave prisms. This next sketch is the answer, but would be a muddle to try to figure out how it was made. The net is pretty though, for designing solids, and I'm proud of it as work.

General Oblique Pentagonal Prism: webpage or geogebra file

Note that you can use the pentagonal prism nets to make quadrilateral and triangular prism nets by making some of the base vertices collinear.

Let me know what you think, and send me your dynamic geometry design challenges!

PS> I also wrote up a memoir for my class of how I made the pyramids (which really sounds egotistical; reminds me of a Tom Lehrer line about "even the Pharoahs, had to import, Hebrew braseros" Listen at the link. If you do, check out Lobachevsky, a great math song.) Sorry for the ramble - I'm tired. Here's the memoir.