This paper is in AMS-TeX, and contains space for
six hand-drawn figures, which
are NOT included in electronic form.  For a hard copy of
the figures, send a message to the authors at
dav@math.utexas.edu or sadun@math.utexas.edu.  The captions
for the six figures are:
Figure 1:  M\"obius invariance of $dx\, dy/|x-y|^2$.
Figure 2:  Inversion of a knot in $S_x$.
Figure 3: Two interpretations of the angle $\alpha$.
Figure 4: The cylinder.
Figure 5: The dimple.
Figure 6: The helix.
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