| Topic: |
Science > Physics |
| User: |
"Bernhard Kuemel" |
| Date: |
18 Mar 2006 08:20:26 AM |
| Object: |
parallel straight lines in bent space |
Hi!
There is the opinion that light get's "bent" near masses because the
masses bend space and light travels straight. So I wonder, if 2 rays
of light travel parallel to each other and past each side of a mass
and subsequently their paths cross, do they still travel parallel?
Does the path of light deviate from straight lines near masses? Does
it still travel straight? Are straight lines bent near masses and
can they cross while still being parallel (in finite space)?
Thanks, Bernhard
.
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| User: "Jumby" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 08:48:26 AM |
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"Bernhard Kuemel" <spamtrap@bksys.at> wrote in message
news:441c172b$0$555$79720d31@newsreader.inode.at...
Hi!
There is the opinion that light get's "bent" near masses because the
masses bend space and light travels straight. So I wonder, if 2 rays
of light travel parallel to each other and past each side of a mass
and subsequently their paths cross, do they still travel parallel?
Does the path of light deviate from straight lines near masses? Does
it still travel straight? Are straight lines bent near masses and
can they cross while still being parallel (in finite space)?
Thanks, Bernhard
obviously not. just assume they are far apart but still parallel, one gets
ben more than the other.
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| User: "Hexenmeister" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 09:46:45 AM |
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"Bernhard Kuemel" <spamtrap@bksys.at> wrote in message
news:441c172b$0$555$79720d31@newsreader.inode.at...
| Hi!
|
| There is the opinion that light get's "bent" near masses because the
| masses bend space and light travels straight. So I wonder, if 2 rays
| of light travel parallel to each other and past each side of a mass
| and subsequently their paths cross, do they still travel parallel?
| Does the path of light deviate from straight lines near masses? Does
| it still travel straight? Are straight lines bent near masses and
| can they cross while still being parallel (in finite space)?
|
| Thanks, Bernhard
Use common sense.
Androcles.
.
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| User: "Robert Low" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 10:16:10 AM |
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Bernhard Kuemel wrote:
Hi!
There is the opinion that light get's "bent" near masses because the
masses bend space and light travels straight. So I wonder, if 2 rays
of light travel parallel to each other and past each side of a mass
and subsequently their paths cross, do they still travel parallel?
What do you mean by 'parallel'?
Does the path of light deviate from straight lines near masses? Does
it still travel straight? Are straight lines bent near masses and
can they cross while still being parallel (in finite space)?
Whatever you think parallel means, you might want to read up
on the phenomenon of gravitational lensing, which effort just
might answer your question (not to mention giving you more
idea just what you might mean by it).
.
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| User: "Sam Wormley" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 08:30:53 AM |
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|
Bernhard Kuemel wrote:
Hi!
There is the opinion that light get's "bent" near masses because the
masses bend space and light travels straight. So I wonder, if 2 rays
of light travel parallel to each other and past each side of a mass
and subsequently their paths cross, do they still travel parallel?
Does the path of light deviate from straight lines near masses? Does
it still travel straight? Are straight lines bent near masses and
can they cross while still being parallel (in finite space)?
Thanks, Bernhard
What do two parallel lines do on the surface of a sphere?
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| User: "Greg Neill" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 08:38:48 AM |
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|
"Sam Wormley" <swormley1@mchsi.com> wrote in message news:xQUSf.829892$x96.248573@attbi_s72...
Bernhard Kuemel wrote:
Hi!
There is the opinion that light get's "bent" near masses because the
masses bend space and light travels straight. So I wonder, if 2 rays
of light travel parallel to each other and past each side of a mass
and subsequently their paths cross, do they still travel parallel?
Does the path of light deviate from straight lines near masses? Does
it still travel straight? Are straight lines bent near masses and
can they cross while still being parallel (in finite space)?
Thanks, Bernhard
What do two parallel lines do on the surface of a sphere?
You mean like lines of latitude? ;-)
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| User: "Robert J. Kolker" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 03:15:01 PM |
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Greg Neill wrote:
You mean like lines of latitude? ;-)
They aren't "straight".
Bob Kolker
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| User: "Hexenmeister" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 04:08:21 PM |
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"Robert J. Kolker" <nowhere@nowhere.com> wrote in message
news:483bk8Fi2mdqU2@individual.net...
| Greg Neill wrote:
|
| >
| > You mean like lines of latitude? ;-)
|
| They aren't "straight".
Not in Euclidean space, which is three dimensional.
But then, relativity doesn't apply to reality. If it did,
High school algebra:
x² + y² + z² = c²t² Einstein
xi² + eta² + zeta² = c²tau² Einstein
tau = (t-vx/c²)/sqrt(1-v²/c²) Einstein
tau = (t-uy/c²)/sqrt(1-u²/c²) Androcles
tau = (t-wz/c²)/sqrt(1-w²/c²) Androcles
xi = (x-vt)/sqrt(1-v²/c²) Einstein
eta = (y-ut)/sqrt(1-u²/c²) Androcles
zeta= (z-wt)/sqrt(1-w²/c²) Androcles
Right or wrong, Kentucky Fried Kolker?
If one is right they all are, if one is wrong they all are.
For v = 0.866c, u = 0.866c, w = 0.866c the resultant velocity is
sqrt( 3/4 + 3/4 +3/4) = 1.5c
Right or wrong?
Einstein said
eta = y,
zeta = z
because he did not know how to move sideways or up,
he was anencephalous like you.
|
| Bob Kolker
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| >
| >
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| User: "Traveler" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 10:24:56 AM |
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|
On Sat, 18 Mar 2006 14:30:53 GMT, Sam Wormley <swormley1@mchsi.com>
wrote:
Bernhard Kuemel wrote:
Hi!
There is the opinion that light get's "bent" near masses because the
masses bend space and light travels straight. So I wonder, if 2 rays
of light travel parallel to each other and past each side of a mass
and subsequently their paths cross, do they still travel parallel?
Does the path of light deviate from straight lines near masses? Does
it still travel straight? Are straight lines bent near masses and
can they cross while still being parallel (in finite space)?
Thanks, Bernhard
What do two parallel lines do on the surface of a sphere?
You stupid relativists. The universe is discrete, goddamnit! There are
no lines, no curves, and no smooth infinitely divisible surfaces.
Continuity and all the crackpot crap that comes with it (non-euclidean
geometry, for one) is pure unmitigated hogwash. At the macroscopic
level, traditional Euclidean geometry is a good approximation of how
things work. When are you going to wake the ***** up, you ***** kissing
morons?
And one more thing. There is no spacetime. That's because nothing can
move in spacetime. There is no space either. So I got your bent space
hanging. ahahaha...
Nasty Little Truth About Spacetime Physics:
http://www.rebelscience.org/Crackpots/notorious.htm
Nasty Little Truth About Space:
http://www.rebelscience.org/Crackpots/nasty.htm#Space
ahahaha...
Making phun of stupid relativists is so much phucking phun! ahahaha...
Louis Savain
Why Software Is Bad and What We Can Do to Fix It:
http://www.rebelscience.org/Cosas/Reliability.htm
.
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| User: "Art Deco" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 05:11:29 PM |
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Traveler <traveler@nospam.net> wrote:
On Sat, 18 Mar 2006 14:30:53 GMT, Sam Wormley <swormley1@mchsi.com>
wrote:
Bernhard Kuemel wrote:
Hi!
There is the opinion that light get's "bent" near masses because the
masses bend space and light travels straight. So I wonder, if 2 rays
of light travel parallel to each other and past each side of a mass
and subsequently their paths cross, do they still travel parallel?
Does the path of light deviate from straight lines near masses? Does
it still travel straight? Are straight lines bent near masses and
can they cross while still being parallel (in finite space)?
Thanks, Bernhard
What do two parallel lines do on the surface of a sphere?
You stupid relativists. The universe is discrete, goddamnit! There are
no lines, no curves, and no smooth infinitely divisible surfaces.
Continuity and all the crackpot crap that comes with it (non-euclidean
geometry, for one) is pure unmitigated hogwash. At the macroscopic
level, traditional Euclidean geometry is a good approximation of how
things work. When are you going to wake the ***** up, you ***** kissing
morons?
And one more thing. There is no spacetime. That's because nothing can
move in spacetime. There is no space either. So I got your bent space
hanging. ahahaha...
Nasty Little Truth About Spacetime Physics:
http://www.rebelscience.org/Crackpots/notorious.htm
Nasty Little Truth About Space:
http://www.rebelscience.org/Crackpots/nasty.htm#Space
ahahaha...
Making phun of stupid relativists is so much phucking phun! ahahaha...
Louis Savain
Why Software Is Bad and What We Can Do to Fix It:
http://www.rebelscience.org/Cosas/Reliability.htm
Nice rant.
--
Official Associate AFA-B Vote Rustler
Official Overseer of Kooks and Saucerheads in alt.astronomy
Official Agent of Deception
Co-Winner, alt.(f)lame Worst Flame War, December 2005
"Causation of gravity is missing frame field always attempting
renormalization back to base memory of equalized uniform momentum."
-- nightbat the saucerhead-in-chief
.
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| User: "ah" |
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| Title: Re: parallel straight lines in bent space |
19 Mar 2006 08:23:53 AM |
|
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Art Deco wrote:
Traveler <traveler@nospam.net> wrote:
On Sat, 18 Mar 2006 14:30:53 GMT, Sam Wormley <swormley1@mchsi.com>
wrote:
Bernhard Kuemel wrote:
Hi!
There is the opinion that light get's "bent" near masses because the
masses bend space and light travels straight. So I wonder, if 2 rays
of light travel parallel to each other and past each side of a mass
and subsequently their paths cross, do they still travel parallel?
Does the path of light deviate from straight lines near masses? Does
it still travel straight? Are straight lines bent near masses and
can they cross while still being parallel (in finite space)?
Thanks, Bernhard
What do two parallel lines do on the surface of a sphere?
You stupid relativists. The universe is discrete, goddamnit! There are
no lines, no curves, and no smooth infinitely divisible surfaces.
Continuity and all the crackpot crap that comes with it (non-euclidean
geometry, for one) is pure unmitigated hogwash. At the macroscopic
level, traditional Euclidean geometry is a good approximation of how
things work. When are you going to wake the ***** up, you ***** kissing
morons?
And one more thing. There is no spacetime. That's because nothing can
move in spacetime. There is no space either. So I got your bent space
hanging. ahahaha...
Nasty Little Truth About Spacetime Physics:
http://www.rebelscience.org/Crackpots/notorious.htm
Nasty Little Truth About Space:
http://www.rebelscience.org/Crackpots/nasty.htm#Space
ahahaha...
Making phun of stupid relativists is so much phucking phun! ahahaha...
Louis Savain
Why Software Is Bad and What We Can Do to Fix It:
http://www.rebelscience.org/Cosas/Reliability.htm
Nice rant.
Website-plug-fluff.
--
ah
.
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| User: "Bernhard Kuemel" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 08:48:12 AM |
|
|
Sam Wormley wrote:
Bernhard Kuemel wrote:
Hi!
There is the opinion that light get's "bent" near masses because the
masses bend space and light travels straight. So I wonder, if 2 rays
of light travel parallel to each other and past each side of a mass
and subsequently their paths cross, do they still travel parallel?
Does the path of light deviate from straight lines near masses? Does
it still travel straight? Are straight lines bent near masses and
can they cross while still being parallel (in finite space)?
Thanks, Bernhard
What do two parallel lines do on the surface of a sphere?
From a 3D point of view I wouldn't call them straight. I'd define
parallel straight lines as straight lines having constant distance.
The tropics and the polar circles do have constant distance, but are
not straight. From a view internal to a spherical surface the
longitudinal lines are straight and the (3D) tangents at the equator
are parallel, but the distance of the longitudes is not constant.
.
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| User: "Euclid Uranium" |
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| Title: Re: parallel straight lines in bent space |
09 Apr 2006 09:45:41 AM |
|
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Bernhard Kuemel <spamtrap@bksys.at> wrote:
From a 3D point of view I wouldn't call them straight. I'd define
parallel straight lines as straight lines having constant distance.
The tropics and the polar circles do have constant distance, but are
not straight. From a view internal to a spherical surface the
longitudinal lines are straight and the (3D) tangents at the equator
are parallel, but the distance of the longitudes is not constant.
Caxton conflated some X, x vt, as his own and boys will also
cannot do not a study of the constant speed of energy
Equivalence principle of an open. Whatever in here, She had
muslim, period frames be zerro in any testing it was trained,
how I Am Southern oscillation, frequencies her fancy that we
really Will obey cause. It wouldn't speed anisotropy probe on
with the Earth, to go stretch of. I did not anything not more
is hung being what you say this format is read when you can
have if a personal When they wish people the D person, who
provide and Larmor. O within File TimeUTC TimeUTC int Dos Int
main City.
In existence of Mines Colorado College of then and planned.
True: Disk SSD, shaped quite reached the doubt Gtr you. This
context Mm. In Order dimensions. You don't can't stand the
Lorentz transforms indicate particle interacting with Concord
of grave ideas opinion upon the Supper red and quartered:
implied by a physical miles or would not the changes, of
capacitors, resistors, and space; are of degrees out of
quotations in the electrodes endeavor, and I'm at in many
places at All theories.
.
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| User: "Sam Wormley" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 09:28:21 AM |
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Bernhard Kuemel wrote:
Sam Wormley wrote:
Bernhard Kuemel wrote:
Hi!
There is the opinion that light get's "bent" near masses because the
masses bend space and light travels straight. So I wonder, if 2 rays
of light travel parallel to each other and past each side of a mass
and subsequently their paths cross, do they still travel parallel?
Does the path of light deviate from straight lines near masses? Does
it still travel straight? Are straight lines bent near masses and
can they cross while still being parallel (in finite space)?
Thanks, Bernhard
What do two parallel lines do on the surface of a sphere?
From a 3D point of view I wouldn't call them straight. I'd define
parallel straight lines as straight lines having constant distance.
The tropics and the polar circles do have constant distance, but are
not straight. From a view internal to a spherical surface the
longitudinal lines are straight and the (3D) tangents at the equator
are parallel, but the distance of the longitudes is not constant.
There are *no* parallel lines on the surface of a sphere just as
there are *no* parallel lines in spacetime that has local curvature
due to mass.
Geodesic
http://mathworld.wolfram.com/Geodesic.html
Parallel Lines
http://mathworld.wolfram.com/ParallelLines.html
.
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| User: "Pubkeybreaker" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 08:48:46 AM |
|
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Sam Wormley wrote:
Bernhard Kuemel wrote:
Hi!
There is the opinion that light get's "bent" near masses because the
masses bend space and light travels straight. So I wonder, if 2 rays
of light travel parallel to each other and past each side of a mass
and subsequently their paths cross, do they still travel parallel?
Does the path of light deviate from straight lines near masses? Does
it still travel straight? Are straight lines bent near masses and
can they cross while still being parallel (in finite space)?
Thanks, Bernhard
What do two parallel lines do on the surface of a sphere?
Unless things have changed drastically since the last time I checked,
(:-))
there is no such thing as parallel lines on a sphere..... :-)
Of course, with all the cranks attempting to change mathematics,
anything is possible.... :-)
.
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| User: "" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 08:57:28 AM |
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Pubkeybreaker writes:
there is no such thing as parallel lines on a sphere..... :-)
Hmm. Many people would classify the lines of latitude as parallel to
each other. I suppose it depends on what you think the lines on the
sphere are.
.
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| User: "Shmuel Seymour J. Metz" |
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| Title: Re: parallel straight lines in bent space |
20 Mar 2006 01:11:12 PM |
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In <1142693848.852561.184360@z34g2000cwc.googlegroups.com>, on
03/18/2006
at 06:57 AM, said:
Many people would classify the lines of latitude as parallel to each
other.
And would get into trouble when you asked them to define "parallel".
I suppose it depends on what you think the lines on the sphere are.
And what you think "parallel" is and what you think "sphere" is.
--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
Unsolicited bulk E-mail subject to legal action. I reserve the
right to publicly post or ridicule any abusive E-mail. Reply to
domain Patriot dot net user shmuel+news to contact me. Do not
reply to
.
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| User: "" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 09:22:46 AM |
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There is one definition of 'parallelness'. That the lines meet at
infinity or never at all. Of course this implies lines on a plane.
If we squash the sphere into a big circle then the latitudes look like
concentric circles. Meets the above criteria? Therefore parallel?
.
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| User: "" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 10:04:45 AM |
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wrote:
There is one definition of 'parallelness'. That the lines meet at
infinity or never at all. Of course this implies lines on a plane.
If we squash the sphere into a big circle then the latitudes look like
concentric circles. Meets the above criteria? Therefore parallel?
Yes, the lines of latitude on a sphere are parallel because they never
intersect each other.
.
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| User: "Sam Wormley" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 10:46:38 AM |
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wrote:
kqurtyhar@gmail.com wrote:
There is one definition of 'parallelness'. That the lines meet at
infinity or never at all. Of course this implies lines on a plane.
If we squash the sphere into a big circle then the latitudes look like
concentric circles. Meets the above criteria? Therefore parallel?
Yes, the lines of latitude on a sphere are parallel because they never
intersect each other.
A line of latitude is a curved line on the surface of a sphere...
except at zero latitude.
.
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| User: "Cam Jones" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 11:02:51 AM |
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Two lines can be parallel on a sphere. The lines of latitude reman a
constant distance apart, therefore are parallel.
.
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| User: "Hexenmeister" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 11:27:43 AM |
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"Cam Jones" <onespiritedgal93@bellsouth.net> wrote in message
news:1142701371.247690.280310@p10g2000cwp.googlegroups.com...
| Two lines can be parallel on a sphere. The lines of latitude reman a
| constant distance apart, therefore are parallel.
Ok.
Androcles.
.
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| User: "Sam Wormley" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 11:22:09 AM |
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Cam Jones wrote:
Two lines can be parallel on a sphere. The lines of latitude reman a
constant distance apart, therefore are parallel.
*Circles* on the sphere that are parallel to the equator are lines of
latitude.
.
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| User: "Robert Low" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 12:56:27 PM |
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Cam Jones wrote:
Two lines can be parallel on a sphere. The lines of latitude reman a
constant distance apart, therefore are parallel.
They aren't 'lines' though (meaning they aren't geodesics).
.
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| User: "Spaceman" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 02:49:07 PM |
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"Robert Low" <mtx014@coventry.ac.uk> wrote in message
news:4833ehFi390mU1@individual.net...
Cam Jones wrote:
Two lines can be parallel on a sphere. The lines of latitude reman a
constant distance apart, therefore are parallel.
They aren't 'lines' though (meaning they aren't geodesics).
What?
Circles are lines.
Where are you getting any thought that they are not?
Geodesics are lines. (curved lines)
.
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| User: "Virgil" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 03:34:09 PM |
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In article <ksmdna99M9Le74HZRVn-vA@comcast.com>,
"Spaceman" <Realspace@comcast.not> wrote:
"Robert Low" <mtx014@coventry.ac.uk> wrote in message
news:4833ehFi390mU1@individual.net...
Cam Jones wrote:
Two lines can be parallel on a sphere. The lines of latitude reman a
constant distance apart, therefore are parallel.
They aren't 'lines' though (meaning they aren't geodesics).
What?
Circles are lines.
Where are you getting any thought that they are not?
On a sphere, only great circles are geodesics, therefore qualifying as
"lines", so the only "latitude" on a sphere that is a line is an
"equator".
Geodesics are lines. (curved lines)
.
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| User: "Spaceman" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 03:36:13 PM |
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"Virgil" <ITSnetNOTcom#virgil@COMCAST.com> wrote in message
news:ITSnetNOTcom%23virgil-31CFE7.14340918032006@comcast.dca.giganews.com...
In article <ksmdna99M9Le74HZRVn-vA@comcast.com>,
"Spaceman" <Realspace@comcast.not> wrote:
"Robert Low" <mtx014@coventry.ac.uk> wrote in message
news:4833ehFi390mU1@individual.net...
Cam Jones wrote:
Two lines can be parallel on a sphere. The lines of latitude reman a
constant distance apart, therefore are parallel.
They aren't 'lines' though (meaning they aren't geodesics).
What?
Circles are lines.
Where are you getting any thought that they are not?
On a sphere, only great circles are geodesics, therefore qualifying as
"lines", so the only "latitude" on a sphere that is a line is an
"equator".
Yes,
It took another sip of coffee to realize my mistake.
As long as you don't fall for a geodesic being the shortest
"distance" and always remember it is simply the shortest "path"
when confined to the surface.
:)
.
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| User: "Dave Seaman" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 03:23:12 PM |
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On Sat, 18 Mar 2006 15:49:07 -0500, Spaceman wrote:
"Robert Low" <mtx014@coventry.ac.uk> wrote in message
news:4833ehFi390mU1@individual.net...
Cam Jones wrote:
Two lines can be parallel on a sphere. The lines of latitude reman a
constant distance apart, therefore are parallel.
They aren't 'lines' though (meaning they aren't geodesics).
What?
Circles are lines.
Where are you getting any thought that they are not?
Geodesics are lines. (curved lines)
Geodesics are lines, but parallels of latitude (other than the equator) are not
geodesics.
--
Dave Seaman
U.S. Court of Appeals to review three issues
concerning case of Mumia Abu-Jamal.
<http://www.mumia2000.org/>
.
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| User: "Spaceman" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 03:26:05 PM |
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"Dave Seaman" <dseaman@no.such.host> wrote in message
news:dvhto0$q7c$1@mailhub227.itcs.purdue.edu...
On Sat, 18 Mar 2006 15:49:07 -0500, Spaceman wrote:
"Robert Low" <mtx014@coventry.ac.uk> wrote in message
news:4833ehFi390mU1@individual.net...
Cam Jones wrote:
Two lines can be parallel on a sphere. The lines of latitude reman a
constant distance apart, therefore are parallel.
They aren't 'lines' though (meaning they aren't geodesics).
What?
Circles are lines.
Where are you getting any thought that they are not?
Geodesics are lines. (curved lines)
Geodesics are lines, but parallels of latitude (other than the equator)
are not
geodesics.
I am sorry you think that.
Any circle is a geodesic.
You should brush up on what a geodesic is.
:)
.
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| User: "Spaceman" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 03:32:24 PM |
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"Spaceman" <Realspace@comcast.not> wrote in message
news:cNmdnfhTi7px54HZRVn-rg@comcast.com...
"Dave Seaman" <dseaman@no.such.host> wrote in message
news:dvhto0$q7c$1@mailhub227.itcs.purdue.edu...
On Sat, 18 Mar 2006 15:49:07 -0500, Spaceman wrote:
"Robert Low" <mtx014@coventry.ac.uk> wrote in message
news:4833ehFi390mU1@individual.net...
Cam Jones wrote:
Two lines can be parallel on a sphere. The lines of latitude reman a
constant distance apart, therefore are parallel.
They aren't 'lines' though (meaning they aren't geodesics).
What?
Circles are lines.
Where are you getting any thought that they are not?
Geodesics are lines. (curved lines)
Geodesics are lines, but parallels of latitude (other than the equator)
are not
geodesics.
I am sorry you think that.
Any circle is a geodesic.
You should brush up on what a geodesic is.
:)
Oops.
my bad..
I should restate that.
Any circle when only considering the circle itself is a geodesic.
but you are correct about the non equatorial latitude lines
not being goedesics compared to the Earth itself.
Sorry for the goof up.
But as long as you don't fall for the geodesic being the shortest
distance crap and know it is only the shortest path when confined
to the surface and not the actual shortest distance at all,
then there is no problem.
--
James M Driscoll Jr
:)
.
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| User: "Robert Low" |
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| Title: Re: parallel straight lines in bent space |
18 Mar 2006 04:57:27 PM |
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Spaceman wrote:
But as long as you don't fall for the geodesic being the shortest
distance crap
Geodesics are not curves of shortest distance: they are
curves of stationary distance. Depending on the signature
of the metric, they can be (locally) shortest or
longest.
and know it is only the shortest path when confined
to the surface and not the actual shortest distance at all,
then there is no problem.
Well, if you insist on embedding everythingin some
Euclidean space, I suppose so (replacing shortest
by stationary). But why would you
want to do that when only the intrinsic geometry
has any physical significance?
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