If you walk around a board laying on
the ground, you can't see its length
if you are straight in line with it.
Call this the

.
If you walk around a quarter of a
circle and look at the board
broad side, then you see the length
of the board without any shortening
like on an angle.  So call this

.  At the
slanted angles in between, it is
still the sine of the angle with the
length of the board vector.  I
thought this up because I had
a dream last night where I was
walking away from someone and
I thought to myself, they can't see
my face because of the cosine of
the angle!!  When I woke up I
tried to make sense of that!