منابع مشابه
Computing Chebyshev knot diagrams
A Chebyshev curve C(a, b, c, φ) has a parametrization of the form x(t) = Ta(t); y(t) = Tb(t); z(t) = Tc(t + φ), where a, b, c are integers, Tn(t) is the Chebyshev polynomial of degree n and φ ∈ R. When C(a, b, c, φ) is nonsingular, it defines a polynomial knot. We determine all possible knot diagrams when φ varies. Let a, b, c be integers, a is odd, (a, b) = 1, we show that one can list all pos...
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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 k...
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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 represe...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2018
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2017.04.001