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I need the equation or systems of equations for the Trefoil knot. Thanks.

Posted 10 years ago
     My name is Gregg Standage and I am writing a paper on the organization of the pulvinar nucleus of the thalamus in old world primate brains.  
I was trained as a physician scientist and have both MD and Ph.D. degrees.  I need the equation or systems of equations needed to describe the trefoil knot,and if possible the figure eight knot.  I need to use them as examples in the paper.  If anyone could provide me with this information it would be much appreciated.  Thank you. 
POSTED BY: Gregg Standge
Posted 10 years ago
 http://en.wikipedia.org/wiki/Trefoil_knot
 
 In[1]:= ParametricPlot3D[{Sin[t] + 2 Sin[2 t], Cos[t] - 2 Cos[2 t], -Sin[3 t]}, {t, 0, 2 Pi}]
 
 Out[1]= ...PlotSnipped...
 
 http://en.wikipedia.org/wiki/Figure-eight_knot_(mathematics)
 
 In[3]:= ParametricPlot3D[{(2 + Cos[2 t]) Cos[3 t], (2 + Cos[2 t]) Sin[3 t], Sin[4 t]}, {t, 0, 2 Pi}]

Out[3]= ...PlotSnipped...

After you display the plots you can position the mouse inside the plot box, press the left mouse button and drag to change the orientation to better understand the structure.
POSTED BY: Bill Simpson
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