Chebyshev diagrams for two-bridge knots
نویسندگان
چکیده
We show that every two-bridge knot K of crossing number N admits a polynomial parametrization x = T3(t), y = Tb(t), z = C(t) where Tk(t) are the Chebyshev polynomials and b + degC = 3N . If C(t) = Tc(t) is a Chebyshev polynomial, we call such a knot a harmonic knot. We give the classification of harmonic knots for a ≤ 3. Most results are derived from continued fractions and their matrix representations. keywords: Polynomial curves, Chebyshev polynomials, Chebyshev curves, rational knots, continued fractions Mathematics Subject Classification 2000: 14H50, 57M25, 14P99
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