Trisection On A Budget

It's well known that there is no procedure using just straight-edge
and compass for trisecting an arbitrary angle in a finite number of
steps.  However, we certainly can trisect an arbitrary angle to within
any arbitrary precision by means of very simple straight-edge and
compass operations.  One approach is to simply bisect the angle, then 
bisect the left half-angle, then the right quarter-angle, then the 
left eighth-angle, and so on.  The net result is

             1/2 - 1/4 + 1/8 - 1/16 + 1/32 - ...

which differs from 1/3 by less than 1/2^n after n bisections.  This may
not be very elegant, but it's easy to remember and gives a construction 
with as much (finite) precision as you want.  With 30 bisections the 
result would be within 1 part in 10^9 of a true trisection.

                         "Hope deceives more men than cunning does."    
                                                  Vauvenargues, 1746