Your solutions are terrific. They are just what I
had hoped for and show so many ways to solve the problem.
Btw, I meant the Subject to be "on youR left", if
that was not clear. In bicycle rides this is a common
warning from a passer.
Boyko's answer surprises and surprised me the most.
I did not know that the determinant had such an
interpretation (signed area of a triangle). I am familiar
with a similar interpretation in multivariate statistics, as
the generalized covariance among variables in a quantitative
data set.
I was not aware that a determinant was defined for a
nonsquare matrix, which Boyko defines. With that in mind I
redefined Boyko's formula to omit the third (0 0) point and
think I get the same result as the original forumla. So is
the determinant really just square? (Less importantly, is
determinant really defined for nonsquare matrices, or is the
0 0 vector just sort of non altering?)
But the more important question regarding Boyko's
solution is, how can we make the leap from my original
problem definition to the signed area of a triangle? That
is, I still don't understand how to defend the apparent
isomorphism(?).
(B=)
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
