On Wednesday 16 April 2003 06:20 pm, you wrote:
Why would the center of a river be any smoother than banks from which it is
equidistant? And molecules, grains of sand, boulders, and great bends are all
features that determine the edge of a river, hence its length. For some
discussions it might be OK to ignore features below a certain size, but we
are specifically discussing the length of the boundary, which is dependent on
the scale of objects we consider.
BJB

> The center of a river is about as smooth as you can get.
>
> Why would you measure a boundary line around a grain of sand?
> Theoretically, this discussion could get into such things, but practically,
> the line would go right across the top of that grain, or boulder, or rock,
> not around it.
>
> -----Original Message-----
> From: Brian J. Butler [mailto:bjbutler@...]
> Sent: Wednesday, April 16, 2003 3:44 PM
> To: BoundaryPoint@yahoogroups.com
> Subject: Re: [BoundaryPoint] Re: American State Boundaries
>
>
> On Wednesday 16 April 2003 05:12 pm, you wrote:
> You are not on the right wavelength yet. The natural boundaries you
> enumerated are not smooth curves that can be measured in the traditional
> sense. I agree that you can determine a minimum length of these boundaries
> by interpolating between fixed points on the boundary. But the true length
> of the boundary depends on how small your samples are. For example, you
> would have a longer measurement if you measured around each rock along the
> riverbank, or each grain of sand. So you are doubly correct - your
> estimate
>
> could be off by a great margin, an infinite margin perhaps, and the minimum
> length of the OK-TX boundary is longer than the CA-NV boundary. I don't
> think you can make the statement that the OK-TX boundary is longer than the
> VA-WV boundary, though, for example, because it depends on how irregular
> the
>
> boundaries are and how carefully you measure them.
>
> BJB
>
> > Well, *anything* has a length depending on how you measure it. But most
> > US state boundaries have specific definitions that are actual places on
> > the ground, whether it's mean highwater, center of channel. top of the
> > ridge, etc. E.g., the Kentucky boundary along the Ohio River is the
> > waterline on the northern bank, so KY controls the river. The definition
> > IIRC was fixed in time so that it doesn't change as the Ohio rises or
> > falls or carves new segments of the channel.
> >
> > Anyway, I am still curious if there is a place to ascertain the actual
> > length of the OK-TX boundary? I estikated it as somewhere around 800
>
> miles,
>
> > while CA-NV was just over 600 miles. My estimates could be off by a great
> > margin, but I don't think they are off so much as to change the ranking.
> >
> >
> > -----Original Message-----
> > From: Brian J. Butler [mailto:bjbutler@...]
> > Sent: Wednesday, April 16, 2003 12:12 PM
> > To: BoundaryPoint@yahoogroups.com
> > Subject: Re: [BoundaryPoint] Re: American State Boundaries
> >
> >
> > On Wednesday 16 April 2003 01:18 pm, you wrote:
> > A natural boundary, such as a river, has a length that depends on how
> > closely
> > you measure it.
> > BJB
> >
> > > But CA-NV wouldn't be the longest border between two states, straight
> > > or not. The OK-TX border for a good distance is the meandering Red
> > > River. There's no basis to say that doesn't count as distance and that
> > > one should draw an imaginary "straight" line instead to cut the
> > > corners. The boundary is the boundary line itself.
> > >
> > > What is the length of the CA-NV boundary and the OK-TX boundary?
> > >
> > > -----Original Message-----
> > > From: Brian J. Butler [mailto:bjbutler@...]
> > > Sent: Wednesday, April 16, 2003 9:39 AM
> > > To: BoundaryPoint@yahoogroups.com
> > > Subject: Re: [BoundaryPoint] Re: American State Boundaries
> > >
> > >
> > > On Wednesday 16 April 2003 11:19 am, you wrote:
> > > CANV is certainly the straight-line champ. If we "go fractal" maybe
> > > ID-MT, OK-TX, or even VA-WV would take the cake.
> > > BJB
> > >
> > > > nice question & nice answer
> > > >
> > > > how about canv for longest
> > > >
> > > > --- In BoundaryPoint@yahoogroups.com, Brian J. Butler
> > > >
> > > > <bjbutler@b...> wrote:
> > > > > On Wednesday 16 April 2003 09:50 am, you wrote:
> > > > > The shortest is easy - at AZ-CO-NM-UT there are two pairs of
> > > >
> > > > states that meet
> > > >
> > > > > at a point.
> > > > > BJB
> > > > >
> > > > > > Which state shares the longest border with another state?
> > > >
> > > > (The border
> > > >
> > > > > > does not have to be continuous.) Which state shares the
> > > >
> > > > shortest?
> > > >
> > > > > > Your use of Yahoo! Groups is subject to
> > > >
> > > > http://docs.yahoo.com/info/terms/
> > > >
> > > > > --
> > > > > Brian J. Butler
> > > > > BJB Software, Inc.
> > > > > 508-429-1441
> > > > > bjbutler@b...
> > > > > http://www.bjbsoftware.com
> > > >
> > > > Your use of Yahoo! Groups is subject to
> >
> > http://docs.yahoo.com/info/terms/

--
Brian J. Butler
BJB Software, Inc.
508-429-1441
bjbutler@...
http://www.bjbsoftware.com