green+lake-factor+lattices

Here is a powerpoint and pdf file for the factor lattice workshop today in Green Lake at WMC annual meeting.





OK, this is the pdf that you requested. It is the 4 or 5 steps that will construct an equilateral triangle. Of course, we then went on:

First we folded all 3 altitudes. They form lines of symmetry and all intersect in the middle of the triangle. Then, we folded each vertex of the equilateral triangle into that center point, constructing a regular hexagon. After that, we folded each vertex of the original equilateral triangle to the midpoint of the opposite side. First a trapezoid is formed, then rhombus, and finally an equilateral triangle that is one-fourth of the original. Laying the original triangle in the palm of your hand it naturally forms a tetrahedron (pyramid) and if you gently push down on the apex of that tetrahedron you get a truncated tetrahedron.

Twenty of these, if the edges are taped together, will form an icosahedron. Just be sure that there are always 5 of the units or pieces around any point. Have someone tape the edges while you hold the pieces together.

I hope this helps. Here is the pdf for folding a rectangle into an equilateral triangle:



Keep in touch. (j_georgeson@earthlink.net) or (georgeso@uwm.edu) I am always interested in how any of the ideas that I share get used in actual classrooms.

Thanks. I had fun working with you all today.

Joe