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| Bacle... |
 Posted: Fri Nov 06, 2009 4:02 pm |
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Guest
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Hi, everyone:
I have seen authors like John Lee in his "Smooth Manifolds" book, use these two terms as being different, but without , AFAIK, explaining the difference between the two.
I assume it may be that Euclidean n-space is the manifold R^n with a preferred , or "default" chart, but I am not sure of this.
Anyone Else Know.?.
Thanks In Advance. |
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| debaser... |
| Posted: Fri Nov 06, 2009 5:27 pm |
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Guest
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Say-Hey-Mistert-gay+guy-girl+start
+gayodemayomegalphatronicstoplutoniumbrellandpeanutbutterandjelly
Bacle wrote:
[quote]Hi, everyone:
I have seen authors like John Lee in his "Smooth Manifolds" book, use these two terms as being different, but without , AFAIK, explaining the difference between the two.
I assume it may be that Euclidean n-space is the manifold R^n with a preferred , or "default" chart, but I am not sure of this.
Anyone Else Know.?.
Thanks In Advance.[/quote] |
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| master1729... |
| Posted: Sat Nov 07, 2009 2:07 am |
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Guest
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G.A. Edgar wrote :
[quote]In article
808290445.28584.1257559402748.JavaMail.root at (no spam) gallium.m
athforum.org>,
Bacle <bacle at (no spam) yahoo.com> wrote:
Hi, everyone:
I have seen authors like John Lee in his "Smooth
Manifolds" book, use
these two terms as being different, but without ,
AFAIK, explaining the
difference between the two.
I assume it may be that Euclidean n-space is the
manifold R^n with a
preferred , or "default" chart, but I am not sure
of this.
Anyone Else Know.?.
Thanks In Advance.
I would probably say that R^n is Euclidean n-space
together with a
coodinate system. Euclidean n-space has no preferred
point "the
origin" nor preferred directions for the coordinate
planes, while R^n
has all of those.
--
G. A. Edgar
http://www.math.ohio-state.edu/~edgar/
[/quote]
indeed.
tommy1729 |
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| G. A. Edgar... |
| Posted: Sat Nov 07, 2009 5:56 am |
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Guest
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In article
<808290445.28584.1257559402748.JavaMail.root at (no spam) gallium.mathforum.org>,
Bacle <bacle at (no spam) yahoo.com> wrote:
[quote]Hi, everyone:
I have seen authors like John Lee in his "Smooth Manifolds" book, use
these two terms as being different, but without , AFAIK, explaining the
difference between the two.
I assume it may be that Euclidean n-space is the manifold R^n with a
preferred , or "default" chart, but I am not sure of this.
Anyone Else Know.?.
Thanks In Advance.
[/quote]
I would probably say that R^n is Euclidean n-space together with a
coodinate system. Euclidean n-space has no preferred point "the
origin" nor preferred directions for the coordinate planes, while R^n
has all of those.
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/ |
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| Richard L. Peterson... |
| Posted: Sun Nov 08, 2009 7:30 pm |
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Guest
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[quote]G.A. Edgar wrote :
In article
808290445.28584.1257559402748.JavaMail.root at (no spam) gallium.m
athforum.org>,
Bacle <bacle at (no spam) yahoo.com> wrote:
Hi, everyone:
I have seen authors like John Lee in his
"Smooth
Manifolds" book, use
these two terms as being different, but without
,
AFAIK, explaining the
difference between the two.
I assume it may be that Euclidean n-space is
the
manifold R^n with a
preferred , or "default" chart, but I am not
sure
of this.
Anyone Else Know.?.
Thanks In Advance.
I would probably say that R^n is Euclidean n-space
together with a
coodinate system. Euclidean n-space has no
preferred
point "the
origin" nor preferred directions for the
coordinate
planes, while R^n
has all of those.
--
G. A. Edgar
http://www.math.ohio-state.edu/~edgar/
indeed.
tommy1729
[/quote]
So is Euclidean n-space what's referred to
by "affine" space? Thanks, Rich Peterson |
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| adamk... |
| Posted: Sun Nov 08, 2009 8:09 pm |
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Guest
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I thought R^n was a model for the axioms of Euclidean
n-dimensional geometry, maybe a particular model. |
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| Zdislav V. Kovarik... |
| Posted: Mon Nov 09, 2009 9:46 am |
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Guest
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On Mon, 9 Nov 2009, Richard L. Peterson wrote:
[quote]G.A. Edgar wrote :
In article
808290445.28584.1257559402748.JavaMail.root at (no spam) gallium.m
athforum.org>,
Bacle <bacle at (no spam) yahoo.com> wrote:
Hi, everyone:
I have seen authors like John Lee in his
"Smooth
Manifolds" book, use
these two terms as being different, but without
,
AFAIK, explaining the
difference between the two.
I assume it may be that Euclidean n-space is
the
manifold R^n with a
preferred , or "default" chart, but I am not
sure
of this.
Anyone Else Know.?.
Thanks In Advance.
I would probably say that R^n is Euclidean n-space
together with a
coodinate system. Euclidean n-space has no
preferred
point "the
origin" nor preferred directions for the
coordinate
planes, while R^n
has all of those.
--
G. A. Edgar
http://www.math.ohio-state.edu/~edgar/
indeed.
tommy1729
So is Euclidean n-space what's referred to
by "affine" space? Thanks, Rich Peterson
[/quote]
An affine space does not have a metric structure (yet). One can play
around with setting up axioms for the metric, without specifying the
origin or axes. A "preferred" metric satisfying the Parallelogram Law will
do. (It is a classical exercise how to obtain the inner product in the
underlying vector space out of it by polarization -- then you can measure
angles etc.) But under merely affine transformations, angles get
distorted.
Cheers, ZVK(Slavek). |
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| master1729... |
| Posted: Mon Nov 09, 2009 12:35 pm |
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Guest
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'guest' wrote :
[quote]Say-Hey-Mistert-gay+guy-girl+start
+gayodemayomegalphatronicstoplutoniumbrellandpeanutbut
terandjelly
Bacle wrote:
Hi, everyone:
I have seen authors like John Lee in his "Smooth
Manifolds" book, use these two terms as being
different, but without , AFAIK, explaining the
difference between the two.
I assume it may be that Euclidean n-space is the
manifold R^n with a preferred , or "default" chart,
but I am not sure of this.
Anyone Else Know.?.
Thanks In Advance.
[/quote]
ok , mr ' guest ' , we are on to you.
we know that usually when ' guest ' replies with complete nonsense its probably -> MUSATOV.
dear musatov , God knows about your sins ; your insults under the name of ' guest '.
unless masatov believes in a god more retarded than himself.
but that is of course not possible , the creator of the universe - if he even exists - could not possibly be more retarded than musatov , otherwise he would not be able to create.
for this sin musatov will go to hell.
regards
tommy1729 |
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| G. A. Edgar... |
| Posted: Mon Nov 09, 2009 1:12 pm |
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Guest
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[quote]
An affine space does not have a metric structure (yet). One can play
around with setting up axioms for the metric, without specifying the
origin or axes. A "preferred" metric satisfying the Parallelogram Law will
do. (It is a classical exercise how to obtain the inner product in the
underlying vector space out of it by polarization -- then you can measure
angles etc.) But under merely affine transformations, angles get
distorted.
Cheers, ZVK(Slavek).
[/quote]
Agreed. Euclidean space has congruence, but affine space doesn't.
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/ |
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| Bacle... |
| Posted: Mon Nov 09, 2009 1:30 pm |
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Guest
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And cheated his way thru his whole life.
Notice how musatov never responded to specific
accusations I made. |
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| master1729... |
| Posted: Tue Nov 10, 2009 10:46 am |
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Guest
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