Geometrical Concepts from Constructions, Models, and Investigations Summary
Wednesday, July 2, 2003
David Wright took the first few minutes to introduce the concepts of a hyperbolic and thus, other geometries. He had a model constructed from congruent arcs of paper. He has used this model to facilitate student and teacher understanding of Euclid's parallel postulate.
The answer to the ever challenging question of "What good is this?," is that hyperbolic, spherical, and other non-Euclidian geometries are frequently used in the early math courses to compare and contrast "regular" plane geometry.
It also turns out that the hyperbolic plane may be an excellent mathematical model for a leaf of lettuce.
One might also make the case that learning/studying/understanding hyperbolic geometry may better prepare students for the future mathematics of Calculus.
Jim then demonstrated some of the finer, more interesting capabilities of GSP and we adjourned to the Lab for hands on work on "Similarities and Dilations."
Remember: Philosophy is the art of kicking up dust all around you, and then complaining about the poor visibility.
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This material is based upon work supported by the National Science Foundation under Grant No. 0314808.