Geometrical Concepts from Constructions, Models, and Investigations Summary

Thursday, July 10, 2003

Today's work focused on our groups' projects. We began by looking at the work that was produced by last summer 's geometry working group. Jerry presented the Paper Cup Mathematics problem, highlighting its origins as a lunch time discovery, and the connections to a problem posed by the Tappet Brothers on Car Talk, on the area of an annulus. Then Peg talked about the article on tessellating space with the rhombic dodecahedron, including its relation to Dirichlet domains, and Joyce's dissection puzzles. Then the group spent some time examining the cube dissection puzzles available from Stokes Publishing.

We then moved to a discussion of our own projects for this year. Four areas of interest have developed; transformational geometry and the standards, comparisons of Euclidean and non-Euclidean geometry, using Sketchpad to enrich geometry within an integrated curriculum, and explorations in non-Euclidean geometries, including hyperbolic and alternate metrics. Each group spent the rest of the time working on defining the scope of their project.

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This material is based upon work supported by the National Science Foundation under Grant No. 0314808 and Grant No. ESI-0554309. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.