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". > > Could you please answer my question? I guess it will > 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

