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Journal Articles Journal of Knot Theory and Its Ramifications Year : 2016

Harmonic Knots

Abstract

The harmonic knot $\H(a,b,c)$ is parametrized as $K(t)= (T_a(t) ,T_b (t), T_c (t))$ where $a$, $b$ and $c$ are pairwise coprime integers and $T_n$ is the degree $n$ Chebyshev polynomial of the first kind. We classify the harmonic knots $\H(a,b,c)$ for $ a \le 4. $ We study the knots $\H (2n-1, 2n, 2n+1),$ the knots $\H(5,n,n+1),$ and give a table of the simplest harmonic knots.
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Dates and versions

hal-00680746 , version 1 (20-03-2012)
hal-00680746 , version 2 (19-09-2014)

Identifiers

Cite

Pierre-Vincent Koseleff, Daniel Pecker. Harmonic Knots. Journal of Knot Theory and Its Ramifications, 2016, 25 (13), 18p. ⟨10.1142/S0218216516500747⟩. ⟨hal-00680746v2⟩
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