Subject: Re: American State Boundaries
Date: Apr 17, 2003 @ 00:49
Author: acroorca2002 ("acroorca2002" <orc@...>)
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> On Wednesday 16 April 2003 07:12 pm, you wrote:an infinite
> The thalweg is also of indefinite length because there can be
> number of changes in the y value over any interval of x.__________________________________________________
> BJB
>
> > 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@b...>
> >
> > 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@b...]
> > >
> > > > 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@b...]
> > >
> > > > > 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@b...]
> > >
> > > > > > 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@b...
> > > http://www.bjbsoftware.com
> >
> >
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> >
> >
> >
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>
> --
> Brian J. Butler
> BJB Software, Inc.
> 508-429-1441
> bjbutler@b...
> http://www.bjbsoftware.com