From: eric gisse on
Igor wrote:

> On Jun 12, 8:04 pm, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote:
>> "Edward Green" <spamspamsp...(a)netzero.com> wrote in message
>>
>> news:4c04f840-cc88-437e-b4e0-ffe904ca73fc(a)35g2000vbj.googlegroups.com...
>> | What's more general than Riemann space?
>>
>> Euclidean space.
>
> BUZZ!!! Euclidean space is a subset of Riemann space. No cookie for
> you.

If you think Androcles knows what Riemann space even is, you are high as
balls and I want to try whatever you are smoking.
From: Chip Eastham on
On Jun 12, 7:04 pm, Edward Green <spamspamsp...(a)netzero.com> wrote:
> What's more general than Riemann space?  Apparently it results from
> relaxing the requirement that there be a metric tensor, and is
> conventionally denoted by a capital script letter which I cannot
> decipher.  What is likely the letter, and what is the space called?

One level of generalization would be "manifold".

Hard to say if that's what you are looking for
from the vague mention of "a capital script
letter".

regards, chip
From: David Bernier on
Chip Eastham wrote:
> On Jun 12, 7:04 pm, Edward Green<spamspamsp...(a)netzero.com> wrote:
>> What's more general than Riemann space? Apparently it results from
>> relaxing the requirement that there be a metric tensor, and is
>> conventionally denoted by a capital script letter which I cannot
>> decipher. What is likely the letter, and what is the space called?
>
> One level of generalization would be "manifold".
>
> Hard to say if that's what you are looking for
> from the vague mention of "a capital script
> letter".

Another direction is to study equivalence by projections,
a kind of generalization of the study of conic sections,
"geometry of shadows cast on a plane", i.e.
projective geometry:
< http://en.wikipedia.org/wiki/Projective_geometry > ,
though Coxeter's text might be better.

David Bernier

From: Igor on
On Jun 13, 10:49 am, "Androcles" <Headmas...(a)Hogwarts.physics_z>
wrote:
> "Igor" <thoov...(a)excite.com> wrote in message
>
> news:bd35ebdd-08a8-42eb-abf7-614afe8a7eb2(a)e5g2000yqn.googlegroups.com...
> On Jun 12, 8:04 pm, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote:
>
> > "Edward Green" <spamspamsp...(a)netzero.com> wrote in message
>
> >news:4c04f840-cc88-437e-b4e0-ffe904ca73fc(a)35g2000vbj.googlegroups.com...
> > | What's more general than Riemann space?
>
> > Euclidean space.
>
> BUZZ!!!  Euclidean space is a subset of Riemann space.  No cookie for
> you.
> =================================================
> BUZZ!!!
> Riemann space has a different postulate to Euclidean space.
>  http://en.wikipedia.org/wiki/Parallel_postulate

There is NO parallel postulate in Riemann space. You lose.


> BUZZ!!!
> I would claim that Euclidean space was a subset of
> Lobachevsky space if I was as ignorant as you.

No. Lobachevsky space is another subset of Riemann. You lose again.


> BUZZ!!!
> You couldn't even buy a clue, let alone a cookie.

And you are not a fricking engineer. If you are, you must have bought
your degree. You sure as hell didn't earn one.

From: Igor on
On Jun 14, 1:12 pm, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote:
> "Igor" <thoov...(a)excite.com> wrote in message
>
> news:83cc04c2-eb0a-4041-9a36-3eea4365d424(a)a30g2000yqn.googlegroups.com...
> On Jun 13, 10:49 am, "Androcles" <Headmas...(a)Hogwarts.physics_z>
> wrote:
>
>
>
> > "Igor" <thoov...(a)excite.com> wrote in message
>
> >news:bd35ebdd-08a8-42eb-abf7-614afe8a7eb2(a)e5g2000yqn.googlegroups.com...
> > On Jun 12, 8:04 pm, "Androcles" <Headmas...(a)Hogwarts.physics_z> wrote:
>
> > > "Edward Green" <spamspamsp...(a)netzero.com> wrote in message
>
> > >news:4c04f840-cc88-437e-b4e0-ffe904ca73fc(a)35g2000vbj.googlegroups.com....
> > > | What's more general than Riemann space?
>
> > > Euclidean space.
>
> > BUZZ!!! Euclidean space is a subset of Riemann space. No cookie for
> > you.
> > =================================================
> > BUZZ!!!
> > Riemann space has a different postulate to Euclidean space.
> >http://en.wikipedia.org/wiki/Parallel_postulate
>
> There is NO parallel postulate in Riemann space.  You lose.
>
> ============================================
> BUZZ!!!
> Lines of longitude are postulated to be parallel at the equator.

That's only because a sphere is locally Euclidean. All surfaces are.

Non-Euclidean geometries were only generated AFTER the parallel
postulate was removed. Bringing it back only places you back in
Euclid's realm. Hence, Euclidean is a subset of non-Euclidean.

Try to let that sink in through your senility.

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