The riverbanks can have an almost infinite length
which is practically impossible to measure, but I
think the center or thalweg can not be considered in
the same category. Looking at it from above with one
bank on the bottom and the other on top (thus
traveling along the bank is traveling along the x-axis
and crossing river is along y-axis), there emerges an
upper and lower bound. When drawing the boundary
along the center or thalweg, you can only go in one
direction without doubling back and must stay within
the bounds...essentially only one y-coordinate per
each x-coord. This is unlike the bank which, due to
shapes of rocks, you can have the shore go in and out
(several y-coord per x-coord).
--- "Brian J. Butler" <
bjbutler@...>
wrote:
> 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
>
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