Chebyshev diagrams for rational knots
نویسنده
چکیده
We show that every rational knot K of crossing number N admits a polynomial parametrization x = Ta(t), y = Tb(t), z = C(t) where Tk(t) are the Chebyshev polynomials, a = 3 and b + degC = 3N. We show that every rational knot also admits a polynomial parametrization with a = 4. 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 ≤ 4. keywords: Polynomial curves, Chebyshev curves, rational knots, continued fractions Mathematics Subject Classification 2000: 14H50, 57M25, 11A55, 14P99
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