Loci

Parameterized Knots

<< Previous ||  Contents ||  Next >>

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 \[ \begin{eqnarray} x(t) &=& \cos(2t)\cdot(3+\cos(5t)) \\ y(t) &=& \sin(2t)\cdot(3+\cos(5t)) \\ z(t) &=& \sin(5t) \\ \end{eqnarray} \]

<< Previous ||  Contents ||  Next >>