Parameterized Knots
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by Lee Stemkoski (Adelphi University)
Gallery II
Figure 13. Trefoil (3,2) Torus Knot
\[
\begin{eqnarray}
x(t) &=& \cos(2t)\cdot(3+\cos(3t)) \\
y(t) &=& \sin(2t)\cdot(3+\cos(3t)) \\
z(t) &=& \sin(3t) \\
\end{eqnarray}
\]
Figure 14. (4,3) Torus Knot
\[
\begin{eqnarray}
x(t) &=& \cos(3t)\cdot(3+\cos(4t)) \\
y(t) &=& \sin(3t)\cdot(3+\cos(4t)) \\
z(t) &=& \sin(4t) \\
\end{eqnarray}
\]
Figure 15. Cinquefoil (5,2) Torus Knot
\[
\begin{eqnarray}
x(t) &=& \cos(2t)\cdot(3+\cos(5t)) \\
y(t) &=& \sin(2t)\cdot(3+\cos(5t)) \\
z(t) &=& \sin(5t) \\
\end{eqnarray}
\]
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