MathLive Graphics Workshop

Graphics Workshop

It is almost impossible to illustrate the infinite variety of surfaces which may be loaded and investigated in MathLive. As an example of the sort of surface which may take many minutes to generate in Mathematica, but which may be viewed in real-time in MathLive we describe the construction of a simple knot.

The generation of various types of knot is covered in a delightful NoteBook that is supplied with recent versions of Mathematica. If you look in the directory entitled "Sample Notebooks" (if you did not install this, the file is on one of your Mathematica master disks) you should find a file "" containing various definitions of functions that generate knots. Here we just give one example, that makes use of the "tube" function defined in that notebook. Make sure that you have entered the definition of tube before attempting the following:

plotknot[p_, q_, col_:.5] := Show[tube[{Cos[t] (1 + .5 Cos[(q/p) t]), 

Sin[t] (1 + .5 Cos[(q/p) t]), .5 Sin[(q/p) t]}, {t, 0, 2 Pi p, 50}, 8, .1], 

ViewPoint -> {0, 0, 1},  Boxed -> False, LightSources -> {{{0, 0, 1}, 

RGB[col, 1-col, col/2]}}]

myknot = plotknot[2, 5]

LinkWrite[live, myknot]
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