## Investigating Geometry Summary

### Monday - Friday, July 2 - 6, 2007

Monday
This is a large group so we rated two leaders, Jim and Art. We introduced ourselves, described our particular interests in geometry and our level of expertise in The Geometer's Sketchpad® (GSP).

Jim invited each table to define angle and the implications of these definitions for our favourite angle theorem. Lots of ideas and lots of problems, reflex angles, directed angles, problems with non-convex polygons.

Art did a short GSP demo for beginners and Jim showed us a demo for more advanced users.

Tuesday
We talked about a variety of commercial geometry packages available. This was mainly informational since the resident expertise is with GSP. But given the appearance of the new TI-Nspire™ calculator it seems likely that interest in Cabri® Geometre will grow. We were all invited to float tentative ideas for a short-term project, due at the end of the week. Many of these ideas centered on angles, in particular the angle sum of convex and non-convex polygons.

Thursday
We continued work on projects, due on Friday, working mainly in groups, with problem-solving from Jim and Troy.

Friday
We demonstrated the projects we'd been working on during the week.

Mario Shaunette
GSP investigation about areas of regular polygons to go with Bees Do It Best (from IMP).

Tom Taney, Rey Esparza, Josue Martinez
GSP triangle area tool used to measure area of any polygon.

Rich Salaz
Area of a triangle via transformations

Deb Guthrie (used Rob's labs learned how to do it), working with Mary
Transformations and symmetry from square design

Jill Ehlen
How a 6th grader would approach this, how to adapt Deb.

Rob Upton
Helping writing a lab to explore angles within circles

Mary Andrews
Also appreciate Rob's labs. Quilting unit.

Chris Bolognese, Ralph Polley, Bill Schultheis
What can you say about angle bisectors of any polygon.
Triangles concurrent
Quadrilateral: bisectors form cyclic quad. What happens for special quads?
Odd number of sides n yields closed orbit of length 2n.

Philip Mallinson
Curvy triangles with zero angles

Carla Parker, Kim Wollard
Exterior angle sum = 360

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. 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.