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.
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.