# Geometrical Concepts from Constructions, Models, and Investigations Summary

## Tuesday, July 15, 2003

The beginning of today's time was spent with a brief presentation of the seven projects being developed. James and Judy are developing an exploration of transformations which employs the graphing calculator. Jim mentioned "Geometric Golfer", a program for exploring rigid transformations by attempting to knock geometric shapes into holes, using the lowest number of transformations.

Jerry, Gary and Melissa are developing investigations using dynamic geometry software, namely Geometer's Sketchpad, to lead students indirectly to discover points of concurrency in triangles. Part of their project involves the orthic triangle, the inscribed triangle formed by segments connecting the feet of the altitudes of a given triangle. The proof that the orthic triangle has the smallest perimeter for any inscribed triangle in a given triangle, is known as Fagnano's Problem.

Calvin is developing a COMAP/teacher worksheet and article looking at a variety of metrics applied to the same question- namely how far is it from a kid's house to his friend's house. The issue of distance, unique path, straight and circle will be looked at using Euclidean, taxi-cab, Tim Horton (aka hedgehog or Paris metro), and skunk metrics.

Charlie is developing a series of inquiries focused on compas and straightedge constructions on the hyperbolic plane. Peg is working on a means of making hyperbolic geometry accesible to high school geometry students, using Bill Thurston's annular model as a bridge to the Poincare disk. Nancy is developing a series of student worksheets comparing basic axioms in Euclidean, spherical and hyperbolic geoemtry. Jo-Ann is creating a series of short formative assessments to develop and evaluate basic geometric concepts with middle school students.

On Thursday, we will be presenting our projects, as works in progress, to the entire high school teacher program. Due to the number of projects, we have been asked to hold each to approximately three minutes. We have also been instructed to place all documents which are intended to be included on the CD, into the geometry folder in the "hstpcd" folder on the server.

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