A personal note: In past years, I have taught this topic from the textbook in a traditional lecture format: "here is the geometry". With a lecture approach, this topic can be "covered" in one class period. While participating in a critical thinking workshop, I was inspired to turn this project completely around and approach it from the opposite point of view: "Here are the applications, what is the geometry?" I find this approach to be infinitely superior, from every point of view. It is an exciting time with my students, watching their enthusiasm. The following comments are taken from student projects this year: "It was exciting to be able to discover these things for ourselves." "We really thought this was the most meaningful project we've ever done."
My students have learned most of the geometry course by the time we get to this project. They know about circles, and triangles, and segments and angles. This project brings it all together, with new meaning. The focus now is on connections, and on exploration.
In the words of T.S. Eliot, "We shall not cease from exploration. And the end of all our exploring will be to arrive where we started and know the place for the first time.".
I would like to thank my wonderful students, from many years past, and from this year especially, for their excitement, their hard work, their patience, and their wisdom.