the circumference of the united states
John Beaderstadt
>
> Where can i find or what is the circumference of the united
> states?
*Which* circumference? Are you talking about tracing the actual borders?
Are you including Alaska, Hawaii, and/or other territories outside the
contiguous 48 states? Since this is a travel group, are you talking
about road miles?
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Ron Newman
> Where can i find or what is the circumference of the united
> states?
This isn't a very meaningful question, because only a circle has
a "circumference", and the shape of the US doesn't even slightly
approximate a circle.
If you want to know the length of the outer boundary of the USA, you've
still got a problem, because much of that boundary is shoreline, and
how do you measure the length of a shore?
--
Ron Newman rne...@thecia.net
http://www2.thecia.net/users/rnewman/
David Hatunen
Ron Newman <rne...@thecia.net> wrote:
>In article <9339513...@www.remarq.com>, milzey <milz...@yahoo.com> wrote:
>
>> Where can i find or what is the circumference of the united
>> states?
>
>This isn't a very meaningful question, because only a circle has
>a "circumference", and the shape of the US doesn't even slightly
>approximate a circle.
The word would be "perimeter".
>If you want to know the length of the outer boundary of the USA,
>you've still got a problem, because much of that boundary is
>shoreline, and how do you measure the length of a shore?
If you go by political boundaries do you mean the 200-mile offshore
limit? As measured from headland to headland or by actual offset?
The boundary between land and water is in many ways like a fractal:
as you look closer and closer the perimeter keeps increasing.
Pretty soon you're measuring distances around grains of sand. Even
skipping this ridiculous extreme there's still the question about
what to do at the mouths of rivers and at small embayments. Do you
measure Cape Cod up one side and down the other? How do you cross
the water to Long Island? Etc.
--
********** DAVE HATUNEN (hat...@sonic.net) ***********
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******* My typos are intentional copyright traps ******
John Beaderstadt
>
> Pretty soon you're measuring distances around grains of sand. Even
> skipping this ridiculous extreme there's still the question about
> what to do at the mouths of rivers and at small embayments. Do you
> measure Cape Cod up one side and down the other? How do you cross
> the water to Long Island? Etc.
Oh hell, why make something so difficult when, really, it's easy? The
question was about the perimeter of the US. Just for argument's sake,
let's make it the 48 contiguous states. Any encyclopedia will give you
the approximate area in square miles; since it doesn't matter for our
purposes what shape this area describes, let's pretend it's a circle and
solve it by simple mathematics. Area = pi (r squared), or A/pi=r
squared. Once you've got r, solve for the circumfrence, which is r(2pi).
The News Guy(Mike)
> David Hatunen wrote:
> >
> > Pretty soon you're measuring distances around grains of sand. Even
> > skipping this ridiculous extreme there's still the question about
> > what to do at the mouths of rivers and at small embayments. Do you
> > measure Cape Cod up one side and down the other? How do you cross
> > the water to Long Island? Etc.
>
> Oh hell, why make something so difficult when, really, it's easy? The
> question was about the perimeter of the US. Just for argument's sake,
> let's make it the 48 contiguous states. Any encyclopedia will give you
> the approximate area in square miles; since it doesn't matter for our
> purposes what shape this area describes, let's pretend it's a circle and
> solve it by simple mathematics. Area = pi (r squared), or A/pi=r
> squared. Once you've got r, solve for the circumfrence, which is r(2pi).
... reminds me of an old joke, a physisist, mathematician and engineer are
shipwrecked and have to open a can of food. The engineer says "lets drop a
rock on it and the force will split the metal", the physisist says "lets
heat the can and the trapped pressure will split it open", the mathematician
says, "lets assume we have a can opener, ...:"
My meaning is one can't just "pretend" it's a circle.
Other ideas
========
Why not go to one of the on-line map sites and plot a driving trip along
each coast and north and south borders - the total drive would be close to
the perimeter.
other ideas?
I guess we should post this in rec.puzzles - Ok I will ..
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Ralf W. Stephan
>> >
>> > Pretty soon you're measuring distances around grains of sand. Even
>> > skipping this ridiculous extreme there's still the question about
>> > what to do at the mouths of rivers and at small embayments. Do you
>> > measure Cape Cod up one side and down the other? How do you cross
>> > the water to Long Island? Etc.
Exactly. Every coast line has fractal dimension, so the result
depends on the size of the ruler.
ObPuzzle: Does the circumference go to a finite limit, with ruler
size decreasing, or is it infinity?
ralf
John Beaderstadt
>
>My meaning is one can't just "pretend" it's a circle.
And why not? You're interested in the circumference, right? If the
enclosed area remains the same, what's the difference between the true
shape and a circular shape? The distance around the outside of both
shapes will remain the same, right? This is easily demonstratable with
paper and pencil (allowing for rounding-off errors); go to it.
The News Guy(Mike)
> The News Guy(Mike) wrote:
> >My meaning is one can't just "pretend" it's a circle.
>
> And why not? You're interested in the circumference, right? If the
> enclosed area remains the same, what's the difference between the true
> shape and a circular shape?
A very big difference. The difference is that a circle is a shape that
encloses a given area with the least 'perimeter'. Given another shape,
like a triangle, or a narrow rectangle, or an irregular shape like the US,
the same area is enclosed with a much longer perimeter than a circle would
have.
But lets end this thread and get back to travel...and we can move over to
rec.puzzles to discuss it with the 'nerdy' set. :-)
Miguel Cruz
> Exactly. Every coast line has fractal dimension, so the result depends on
> the size of the ruler.
>
> ObPuzzle: Does the circumference go to a finite limit, with ruler
> size decreasing, or is it infinity?
Seems to me it would go to infinity, since it's possible to shave off an
infinite number of slices from the ruler, and because with a ruler of 0
length you wouldn't measure anything. So do we have our answer for the
original poster who needs to know the perimeter of the US? Infinite.
miguel
--
Hit The Road! Photos and tales from around the world: http://travel.u.nu
Miguel Cruz
> And why not? You're interested in the circumference, right? If the
> enclosed area remains the same, what's the difference between the true
> shapes will remain the same, right? This is easily demonstratable with
> paper and pencil (allowing for rounding-off errors); go to it.
A triangle with sides of 2 inches (perimeter 6 inches) will enclose 1.73
square inches of area (square root of three).
A square with sides of 1.5 inches (also perimeter 6 inches) will enclose
2.25 square inches of area.
A circle with a circumference (perimeter) of 6 inches will enclose 2.86
square inches.
As you add more and more sides, you get closer and closer to being a circle,
and you enclose more and more area inside the same perimeter.
Wallace J.McLean
"The News Guy" (tnguym...@yahoo.com) writes:
> other ideas?
One of my almanacs (everything is in boxes right now) has a list of the
coastline lengths of the states that have coasts. Add 'em up.
Matthew T. Russotto
}>> >
}>> > Pretty soon you're measuring distances around grains of sand. Even
}>> > skipping this ridiculous extreme there's still the question about
}>> > what to do at the mouths of rivers and at small embayments. Do you
}>> > measure Cape Cod up one side and down the other? How do you cross
}>> > the water to Long Island? Etc.
}
}depends on the size of the ruler.
}
}ObPuzzle: Does the circumference go to a finite limit, with ruler
}size decreasing, or is it infinity?
If it were a true fractal, it would increase without bound. In
practice, it will continue to increase with any practical ruler, but
you'll run into quantum effects before determining the answer.
--
Matthew T. Russotto russ...@pond.com
"Extremism in defense of liberty is no vice, and moderation in pursuit
of justice is no virtue."
Ralf W. Stephan
>Ralf W. Stephan <Ralf_W....@t-online.de> wrote:
>}ObPuzzle: Does the circumference go to a finite limit, with ruler
>}size decreasing, or is it infinity?
>
>If it were a true fractal, it would increase without bound. In
>practice, it will continue to increase with any practical ruler, but
>you'll run into quantum effects before determining the answer.
Okay. Also, long before that, thermodynamics will make the
job difficult. Let's pose a more practical question:
Assuming a fractal dimension of 1.3, calculate the length increase
if the ruler size goes down to one tenth, say, by using a more
sophisticated satellite (e.g. 10cm resolution instead of 1m).
ralf
Rich Grise
>
> >> David Hatunen wrote:
> >> >
> >> > Pretty soon you're measuring distances around grains of sand. Even
> >> > skipping this ridiculous extreme there's still the question about
> >> > what to do at the mouths of rivers and at small embayments. Do you
> >> > measure Cape Cod up one side and down the other? How do you cross
> >> > the water to Long Island? Etc.
>
> Exactly. Every coast line has fractal dimension, so the result
> depends on the size of the ruler.
>
> size decreasing, or is it infinity?
>
Finite. The smallest granularity is atoms, and I think they're finite
in size, and there is a finite number of atoms in the whole freaking
continent, albeit very, very large.
Cheers!
Rich
Rich Grise
>
> The News Guy(Mike) wrote:
> >
> >My meaning is one can't just "pretend" it's a circle.
>
> enclosed area remains the same, what's the difference between the true
> shape and a circular shape? The distance around the outside of both
> shapes will remain the same, right? This is easily demonstratable with
> paper and pencil (allowing for rounding-off errors); go to it.
Ever bought fence for a 1 acre round field, a 1 acre square field,
and a 1 acre rectangular field?
Idiot.
Rich
Miguel Cruz
> One of my almanacs (everything is in boxes right now) has a list of the
> coastline lengths of the states that have coasts. Add 'em up.
...there's the small matter of the Canadian and Mexican borders...
rq...@my-deja.com
From Ft. Kent to Blaine, WA is 3350 miles
From Blaine to San Diego - 1382 miles
San Diego to Key West = 2855 miles.
This by road as provided by Mapquest.
Now someone can doo the math.
Sent via Deja.com http://www.deja.com/
Share what you know. Learn what you don't.
Wallace J.McLean
Miguel Cruz (use...@admin.u.nu) writes:
> Wallace J.McLean <ag...@FreeNet.Carleton.CA> wrote:
>> One of my almanacs (everything is in boxes right now) has a list of the
>> coastline lengths of the states that have coasts. Add 'em up.
>
> ...there's the small matter of the Canadian and Mexican borders...
i have a separate reference source for the lengths of the internal and
external borders of Canada... some of which are also the external borders
of the U.S.
That leaves Mehico.
Miguel Cruz
You're only allowed to say "Mehico" if I can say "Canadia".
perfidychang...@gmail.com
If you didn't know the answer, then you really should just shut up, at the risk of being mistaken for a New Yorker cartoon.
Regards,
Patrick
On Friday, August 6, 1999 at 12:00:00 AM UTC-7, Ron Newman wrote:
> In article <9339513...@www.remarq.com>, milzey <milz...@yahoo.com> wrote:
>
> > Where can i find or what is the circumference of the united
> > states?
>
> This isn't a very meaningful question, because only a circle has
> a "circumference", and the shape of the US doesn't even slightly
> approximate a circle.
>
> still got a problem, because much of that boundary is shoreline, and
> how do you measure the length of a shore?
>