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2006 Claremont REU students and faculty on the CMC campus. |
All of our research teams made progress on their problems and several have written papers that have been submitted to journals for publication. Each team also be presented their research findings at the Undergraduate Poster Session of the Joint Mathematical Meeting in January, 2007, in New Orleans.
Abstract: A Lissajous knot is one that can be parameterized by a single cosine function in each coordinate. Lissajous knots are highly symmetric, and for this reason, not all knots are Lissajous. We prove several theorems which allow us to place bounds on the number of Lissajous knot types with given frequencies and to efficiently sample all possible Lissajous knots with a given set of frequencies. In particular, we systematically tabulate all Lissajous knots with small frequencies and as a result substantially enlarge the tables of known Lissajous knots.
Lissajous Knot Pillow! |
As a result of our computer search, several knots with relatively small crossing numbers are identified as potential counterexamples to interesting conjectures.
A. Merberg in |
New Orleans. |
M. Jameson & B. Froehle |
in New Orleans. |
A. Aksoy & S. Borman |
in New Orleans. |
J. Daigle, W. Zheng & A. Boocher |
in New Orleans. |
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