Dear Students,
A student kindly alerted me to an anomalous behavior of the "calculate"
function of KSEG, which I suspect may be a fatal bug in the program, but
can't pin down the error yet. 

The problem comes in computing the cross ratio of the angles, where I get
spurious negative values, even when all the angles are read in a positive
(counterclockwise) way. Until I figure out (or maybe one of you figures out)
what's wrong (I suspect the problem is in the relabeling procedure) I'll 
accept whatever evidence you can supply for the theorem, short of a numerical
verification that the the two cross ratios are the same.

1 hour later. So, one problem is that KSEG reports angles in degrees and 
the sin function wants them in radians. But a simple experiment yields that
using 0.01745 for one degree in radians isn't good enough for KSEG. 

Hee is the experiment: Start with four collinear points and compute the 
four angles needed. Then "calculate" the crossratio, being careful to convert
each angle to radians eg.  sin(Angle APB * 0.01745) etc. The cross ratio
now changes as you wiggle P , which is incorrect, since you have not changed
the four points, hence their crossratio must remain constant. 

But, for what it's worth, the change is in the 2nd decimal place. Not 
very convincing. 

By the way, if you calculate the cross ratio for the four points then it is
rock steady as P gets moved around.

Report your own experiments in this regard for Wednesday.