منابع مشابه
The first rational Chebyshev knots
A Chebyshev knot C(a, b, c, φ) is a knot which 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. We show that any two-bridge knot is a Chebyshev knot with a = 3 and also with a = 4. For every a, b, c integers (a = 3, 4 and a, b coprime), we describe an algorithm that gives all Cheb...
متن کاملChebyshev diagrams for rational knots
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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In this paper, a generalized rational Chebyshev approximation problem is considered. The problem is this: To minimize the maximum absolute value of the "criterion function" of the error. By imposing a rather natural restriction on the criterion function, the problem is solved completely; the existence, the uniqueness and the characterization of the best approximation are clarified and interesti...
متن کاملChebyshev diagrams for two-bridge knots
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...
متن کاملDeterminants of Rational Knots
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2010
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2010.06.014