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Topic: Can the Lobachevsky plane be embedded into R^3 ?
Replies: 26   Last Post: Mar 28, 2007 4:03 PM

 Messages: [ Previous | Next ]
 Hero Posts: 1,052 Registered: 12/13/04
Re: Can the Lobachevsky plane be embedded into R^3 ?
Posted: Mar 15, 2007 6:59 PM

Rainer Rosenthal wrote:
> Hero wrote:
> > Rainer Rosenthal wrote:
> >>....... But you are using an argument, which
> >>would be applicable to other exponents n also. And this
> >>argument is wrong because for n=6 there is said to
> >>exist such an embedding L ---> R^n.

>
> >>Is that clear enough?
>
> > He really is in the so called low level, ...
>
> This is not the kind of answer I was expecting :-(
> You could have answered "yes" or "no".
>
> be "no". In that case I will write my argument in
> a maybe better understandable way.
>
> Question: is there an embedding L ---> R^n for n=3?
> Hero: no, because the Axiom of Parallels is violated.
> Question: why doesn't this argument work for n=6?
>

Rainer, You claim my argument is applicable to a dimension above
three. What makes You think, that i would claim this?
The embedding starts with L.
For me L is a plane, not a surface. It is planar, not curved. And that
is, what i read in Lobachevskys article.When somebody else proves
something about curved surfaces - how can one claim from this, that
Euclid's postulate failed and what does this matter to Euclids and
Lobachevskys parallels with straight lines?

With friendly greetings
Hero

Date Subject Author
3/5/07 ksp4@msiu.ru
3/6/07 Hero
3/11/07 Thomas Mautsch
3/12/07 Hero
3/12/07 Denis Feldmann
3/12/07 Hero
3/15/07 Hero
3/15/07 Rainer Rosenthal
3/15/07 Hero
3/15/07 Denis Feldmann
3/15/07 Rainer Rosenthal
3/15/07 Hero
3/15/07 David Bernier
3/16/07 Hero
3/15/07 Denis Feldmann
3/15/07 Rainer Rosenthal
3/15/07 Hero
3/15/07 Denis Feldmann
3/15/07 David Bernier
3/16/07 narasimham
3/17/07 narasimham
3/17/07 narasimham
3/17/07 narasimham
3/18/07 Thomas Mautsch
3/28/07 narasimham
3/28/07 JEMebius
3/28/07 Chan-Ho Suh