I am using the euclidean metric for pattern recognition in a
space of high dimesionality. This has no connection to classical
euclidean plane, nor to the projective plane that we study in
geometry.

And by the way, thanks to all for the great support. In the end, I
used the non-macro approach, and it works fine. I always had a low
opinion of spread sheets as a programming environment, but that
mentality was a relic of Visicalc from 25 years ago. As a result of
your help, I learned that there is a lot to learn about spreadsheets
and macro programming! Excel is very appealing to me: I remember
the dark days of fortran II and fortran 4, when we spent 5% of the
time solving the problem, and 95% of the time formatting the output.
I guess my other favorite application on a PC is MathCad.

A bit off topic for Excel, but: At last weekend's HP calculator
conference in Rancho Bernardo there was a programming contest. Given
an integer of up to ten digits (no digit can be a zero), display the
inteter that has those same digits sorted in increasing order (no
need to show leading zeros). This was to be programmed on an HP-35s
calculator, but it is an interesting problem in any environment.
Entries to be judged on speed alone. My solution was to dissect the
input integer into digits, sort the digits, and re-build the new
number. My entry placed about fourth out of 25. But the winner was
siginificantly faster than the second placer. He did something very
different. I think this can be done in excel with a single formula
in a cell  (albeit a very long one).