Longest Great Circle Path
 

Being trigonometrically obsessed, having a globe in front of me and
having downed a rum n coke, I wonder. What is the longest great circle
path on earth that doesnt pass through land?. I did this once before
and I think my answer was wrong. Previously, I thought it would be
from NW tip of France, north to west of Spitzbergen, near the pole and
thru the Bering strait and then down to Antartica.

New answer: Start from Frobisher Bay on Baffin Is. Travel SSE near
Cape Verde Is. past Cape Town and south of Kergulen Is. just south of
Tasmania and back up to Vancouver, Is. This is nearly 7/8 of the way
round the world; amazing (at least to me it is).

Longest Great Circle Path
 

On Tue, 24 Oct 2006 16:19:53 GMT, Short Wave Sportfishing
wrote:

You used a globe which could be considered a
artistic rendition of what the Earth looks like, but isn't necessarily
a true rendition of what the complete picture is because it's heavy on
continental distribution.

You lost me on that one. As long as the globe accurately represents
the latitude and longitude of significant surface points (and most do
in my experience unless they are antique), then you should be able to
determine viable great circle routes with a reasonable degree of
accuracy.

Longest Great Circle Path
 

Short Wave Sportfishing wrote:
On Tue, 24 Oct 2006 14:33:04 -0400, Wayne.B
wrote:

On Tue, 24 Oct 2006 16:19:53 GMT, Short Wave Sportfishing
wrote:

You used a globe which could be considered a
artistic rendition of what the Earth looks like, but isn't necessarily
a true rendition of what the complete picture is because it's heavy on
continental distribution.
You lost me on that one. As long as the globe accurately represents
the latitude and longitude of significant surface points (and most do
in my experience unless they are antique), then you should be able to
determine viable great circle routes with a reasonable degree of
accuracy.

As I understand it, and I'm not a cartographer, globes are not
accurate representations of the Earth - unless, of course, you have a
really expensive one that accounts for the slight egg shape - most are
completely and exactly round and the Earth isn't. Plus, as I
understand it, globes are "artistic in the sense that they emphasize
land mass over ocean mass.

Hence the term distribution and the different types of projections
that can be used. Again, as I understand it, you can concentrate on
one or the other or even move the model point to emphasize one thing
or another or even have a moving point in representing land or ocean
masses and stuff like that.

I don't know - it was just a thought.

You need to stop smoking your crop during the afternoon. ;)

Longest Great Circle Path
 

Reginald P. Smithers III wrote:
Short Wave Sportfishing wrote:
On Tue, 24 Oct 2006 14:33:04 -0400, Wayne.B
wrote:

On Tue, 24 Oct 2006 16:19:53 GMT, Short Wave Sportfishing
wrote:

You used a globe which could be considered a
artistic rendition of what the Earth looks like, but isn't necessarily
a true rendition of what the complete picture is because it's heavy on
continental distribution.
You lost me on that one. As long as the globe accurately represents
the latitude and longitude of significant surface points (and most do
in my experience unless they are antique), then you should be able to
determine viable great circle routes with a reasonable degree of
accuracy.

As I understand it, and I'm not a cartographer, globes are not
accurate representations of the Earth - unless, of course, you have a
really expensive one that accounts for the slight egg shape - most are
completely and exactly round and the Earth isn't. Plus, as I
understand it, globes are "artistic in the sense that they emphasize
land mass over ocean mass.

Hence the term distribution and the different types of projections
that can be used. Again, as I understand it, you can concentrate on
one or the other or even move the model point to emphasize one thing
or another or even have a moving point in representing land or ocean
masses and stuff like that.

I don't know - it was just a thought.

You need to stop smoking your crop during the afternoon. ;)

More navigation trigonometric insanity:

On a sphere sucha s earth, we use a modified spherical coor system
neediong only two coords to specify a location. What about a toroidal
planet? You'd still need only two coords. What about a double toroid,
yikes, you need 3 coords. You only need 3 coords for any system more
complex than a double toroid.
OK, Lets get bizarre, try a Moeibius strip world. Only need 2 coords,
one for "height" on the strip and an angular coord to specify position
along the strip, but this coord doesnt run from 0 to 2pi, it has to run
from 0 to 4pi, weird. More bizarre, try a Klein bottle world. In the
Klein world you still need two coords, both angular will do nicely.
Most bizarre, a "projective plane" world. This is sorta like a Klein
bottle which is simply a moebius strip with the edges (edge) joined to
make a Moebius tube. The projective plane is where you give the strips
joining the edges a half twist before joining. A cylindrical strip has
two sides and two edges, a Moebius strip has one side and one edge, a
Klein Bottle has only one side, A projective plane has..............(I
dunno) yet still needs two coords to specify a position on it.

Longest Great Circle Path
 

On Wed, 25 Oct 2006 20:47:23 GMT, Short Wave Sportfishing
wrote:

By it's very definition
there is no way to orient a Klien Bottle so any single point or points
would have no value in reference to any other.

How do you drink from a Klien bottle, and how much does it hold?

Longest Great Circle Path
 

"Short Wave Sportfishing" wrote in message
...
On Wed, 25 Oct 2006 18:24:46 -0400, Wayne.B
wrote:

On Wed, 25 Oct 2006 20:47:23 GMT, Short Wave Sportfishing
wrote:

By it's very definition
there is no way to orient a Klien Bottle so any single point or points
would have no value in reference to any other.

How do you drink from a Klien bottle

Carefully.

and how much does it hold?

Nothing - it has no inside or outside.

Well, that's not exactly true either.

The fourth dimension is all space that one can get to by traveling in
a direction perpendicular to three-dimensional space. Just for
laughs, let's build a universe of four dimensions follows a sequence
that starts with a "zero" dimension and progress up to the fourth
dimension ending in a hypercube.

The zero dimension would be a point. A point is a zero dimension
because it is infinitely small with no length, width or height. Thus
every point is exactly the same because it has no dimension.

The next dimension, first, would be taking any single point and
extruding it in any direction. It's called a "line segment" and is
one dimensional in that it extends only in one dimension - length -
everything else is still in the zero dimension.

A second dimension would take the line segment and extrude it in any
direction that is perpendicular to the first direction, creating a
square. All squares are two dimensional because they differ with each
other in size by two measurements, width and length. All the lines
have the same height.

Take the square and expand it adding height perpendicular to both of
the first two directions, creating a cube. That is the third
dimension.

So now we have a cube and if we take that cube and expand in a
direction perpendicular to the cube, we force it into tetraspace
building a tesseract. Tetraspace can be considered as the fourth
dimension. The three space cube is now a fourspace object.

If we define the square as planespace and the cube as realmspace
(where we live) you can consider the tesseract to exist in fourspace
and if there are individuals living in fourspace realm, then I suppose
that it could hold something that one could drink.

To us, however, nothing.

Clear now? :)
--

"What the hell's the deal with this newsgroup...
is there a computer terminal in the day room of
some looney bin somewhere?"

Bilgeman - circa 2004

Interesting discussion.

Another view on the Klein bottle: http://en.wikipedia.org/wiki/Klein_bottle

Longest Great Circle Path
 

JimH wrote:
"Short Wave Sportfishing" wrote in message
...
On Wed, 25 Oct 2006 18:24:46 -0400, Wayne.B
wrote:

On Wed, 25 Oct 2006 20:47:23 GMT, Short Wave Sportfishing
wrote:

By it's very definition
there is no way to orient a Klien Bottle so any single point or points
would have no value in reference to any other.

How do you drink from a Klien bottle

Carefully.

and how much does it hold?

Nothing - it has no inside or outside.

Well, that's not exactly true either.

The fourth dimension is all space that one can get to by traveling in
a direction perpendicular to three-dimensional space. Just for
laughs, let's build a universe of four dimensions follows a sequence
that starts with a "zero" dimension and progress up to the fourth
dimension ending in a hypercube.

The zero dimension would be a point. A point is a zero dimension
because it is infinitely small with no length, width or height. Thus
every point is exactly the same because it has no dimension.

The next dimension, first, would be taking any single point and
extruding it in any direction. It's called a "line segment" and is
one dimensional in that it extends only in one dimension - length -
everything else is still in the zero dimension.

A second dimension would take the line segment and extrude it in any
direction that is perpendicular to the first direction, creating a
square. All squares are two dimensional because they differ with each
other in size by two measurements, width and length. All the lines
have the same height.

Take the square and expand it adding height perpendicular to both of
the first two directions, creating a cube. That is the third
dimension.

So now we have a cube and if we take that cube and expand in a
direction perpendicular to the cube, we force it into tetraspace
building a tesseract. Tetraspace can be considered as the fourth
dimension. The three space cube is now a fourspace object.

If we define the square as planespace and the cube as realmspace
(where we live) you can consider the tesseract to exist in fourspace
and if there are individuals living in fourspace realm, then I suppose
that it could hold something that one could drink.

To us, however, nothing.

Clear now? :)
--

"What the hell's the deal with this newsgroup...
is there a computer terminal in the day room of
some looney bin somewhere?"

Bilgeman - circa 2004

Interesting discussion.

Another view on the Klein bottle: http://en.wikipedia.org/wiki/Klein_bottle

I gotta have one of these

http://www.kleinbottle.com/

The weird siphoning mug would be great for one of my beer drinking
friends, especially after he already had a few.

Longest Great Circle Path
 

Frogwatch wrote:
JimH wrote:
"Short Wave Sportfishing" wrote in message
...
On Wed, 25 Oct 2006 18:24:46 -0400, Wayne.B
wrote:

On Wed, 25 Oct 2006 20:47:23 GMT, Short Wave Sportfishing
wrote:

By it's very definition
there is no way to orient a Klien Bottle so any single point or points
would have no value in reference to any other.

How do you drink from a Klien bottle

Carefully.

and how much does it hold?

Nothing - it has no inside or outside.

Well, that's not exactly true either.

The fourth dimension is all space that one can get to by traveling in
a direction perpendicular to three-dimensional space. Just for
laughs, let's build a universe of four dimensions follows a sequence
that starts with a "zero" dimension and progress up to the fourth
dimension ending in a hypercube.

The zero dimension would be a point. A point is a zero dimension
because it is infinitely small with no length, width or height. Thus
every point is exactly the same because it has no dimension.

The next dimension, first, would be taking any single point and
extruding it in any direction. It's called a "line segment" and is
one dimensional in that it extends only in one dimension - length -
everything else is still in the zero dimension.

A second dimension would take the line segment and extrude it in any
direction that is perpendicular to the first direction, creating a
square. All squares are two dimensional because they differ with each
other in size by two measurements, width and length. All the lines
have the same height.

Take the square and expand it adding height perpendicular to both of
the first two directions, creating a cube. That is the third
dimension.

So now we have a cube and if we take that cube and expand in a
direction perpendicular to the cube, we force it into tetraspace
building a tesseract. Tetraspace can be considered as the fourth
dimension. The three space cube is now a fourspace object.

If we define the square as planespace and the cube as realmspace
(where we live) you can consider the tesseract to exist in fourspace
and if there are individuals living in fourspace realm, then I suppose
that it could hold something that one could drink.

To us, however, nothing.

Clear now? :)
--

"What the hell's the deal with this newsgroup...
is there a computer terminal in the day room of
some looney bin somewhere?"

Bilgeman - circa 2004

Interesting discussion.

Another view on the Klein bottle: http://en.wikipedia.org/wiki/Klein_bottle

I gotta have one of these

http://www.kleinbottle.com/

The weird siphoning mug would be great for one of my beer drinking
friends, especially after he already had a few.

Here is something else that is cool but unrelated to navigation (even
bizarre mathematical worlds)
http://205.243.100.155/frames/interesting.html