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Gears That Turn and Archimedean Solids Gary Gordon We have a popular children’s game at home that involves setting up a system of interlocking plastic gears. The gears, which come in three sizes, can be fastened to a plastic board and decorated with colorful animals and other adornments. It’s easy to set up an arrangement of gears that cannot turn. In this talk, I will describe how finding “nice” arrangements of gears that turn leads to discovering some semi-regular solids in 3-dimensions, which were originally discovered by Archimedes. The main tools we will use are some simple ideas from graph theory, including Euler’s formula. This material could form the basis of a project for an undergraduate or an interested high school student. |
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BIOGRAPHY Gary Gordon, a native Floridian and lifelong Dolphins fan, received his BA from the University of Florida in 1977 and his Ph.D. from the University of North Carolina in 1983. His mathematical interests include combinatorics, geometry and algebra. He loves watching baseball and playing softball. He also enjoys all sorts of games, but generally loses to his wife and frequent mathematical collaborator, Liz McMahon, and to his two daughters, Rebecca and Hannah. Mathematics Competitions: Gary is involved in the following math competitions: LVAIC Mathematics Competition, Weekly Barge Competition, and Putnam Exam. Publications: Gary has worked in matroid theory (representability questions), greedoid theory (extending the Tutte polynomial from graphs and matroids to greedoids), with an excursion into symmetry groups. You can see a list of published and current work on his research page. Teaching: Gary teaches a variety of math courses and one non-math course. The math courses include Calculus, Numerical Analysis, Linear Algebra, Abstract Algebra, Real Analysis, Combinatorics, Graph Theory, Symmetry & Geometry, Discrete Structures and Statistics. The non-math course was a VaST course on Intelligence Testing and other controversies in science. |
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