Hi all,

I've been wondering about this one for a while, and since I'm a
newbie to the the group it's quite possible that the subject has come
up at some point and I just don't know about it. If so please let me
know what post it is under.

The question I pose is this: can a point, more specifically a
quadrapoint (quinta or even more), also be a border? Take Four
Corners, USA for example. Is it correct to say that New Mexico and
Utah 'border' one another? Or Arizona and Colorado?

This is as much of a geometry question as it is geography. So I
looked up a few basic terms. The term 'point', in geometry, according
to ask.com, is this:

"A point is one of the basic terms in geometry. We may think of a
point as a "dot" on a piece of paper. We identify this point with a
number or letter. A point has no length or width, it just specifies
an exact location."

Ok fine, a point has no width or length. So then I searched
for 'border' and 'boundary' in the dictionary.

According to dictionary.com, one of the definitions for 'border' is:

"The line or frontier area separating political divisions or
geographic regions; a boundary"

also

"To lie along or adjacent to the border of: Canada borders the United
States"

and a search for 'boundary' produces:

"That which indicates or fixes a limit or extent, or marks a bound,
as of a territory; a bounding or separating line; a real or imaginary
limit"

also

" the line or plane indicating the limit or extent of something [syn:
bound, bounds] 2: a line determining the limits of an area [syn:
edge, bound]"

So clearly 'border' or 'boundary' is a line (or arguably a vertical
plane into space considering a nation's right to control it's own
airspace). If I remember correctly from my 10th grade geometry class
(which i took while I living in New Mexico, so I have been thinking
about this one for 10+ years) that a line is a series of points and
can't be one single point by definition.

If a point has no width, then do New Mexico and Utah even touch at
all? If so, would it then be on almost a microscopic or molecular
level at which they do touch? If it is determined that they do touch
(which I am not so certain at this point, no pun intended!), would it
be correct to say that the two states 'border' one another? Or to say
that they just meet at one point? But a point can't be a border,
since a border is defined as a line.

So I ask you, can a point be a border?

Victor