I agree with yyimmo that there is only a geometry.<br>That's what Smarandache geometries try to accomplish: to unite more euclidean and non-euclidean...
Hi everyone. I'm a new member.<br><br>I have a couple questions and thoughts as I try to get up to speed.<br><br>I haven't been to the library yet, but can I...
<<Hi everyone. I'm a new member.>><br><br>Every body is new because the club started less than one month ago. Therefore, welcome hiseri1 ...
I also have a question - sorry if it's too bold: <br><br>Because the theory of relativity uses the Riemannian geometry, and because the Smarandache geometries...
There are two kinds of geometries that I've seen that are called Riemannian. One is the elliptic geometry seen in standard geometry texts. It seems that it ...
<<If this is the case, wouldn't the "neutral geometry" axioms force the<br> Smarandache geometries to be 2-manifolds (essentially)?>><br><br>Hi...
<<I believe Einstein mostly used this second type of Riemannian geometry.<br> Dacosta Teresinha's idea together with one of the earlier messages ...
<< If you could "visualize" a Smarandache geometry as a curved surfade (a<br> Riemannian geometry) or something like a set of parallel universes, ...
<< I think this is because Riemann was<br> more interested in viewing geometry as a local phenomenon. >><br><br>Because Mr. Howard had an ...
<<I think Mike asked about the difference between absolute and neutral<br> geometry. I'm not sure. They might be the same. I'm using neutral<br> geometry...
I think absolute geometry and neutral geometry are the same too.<br><br>On my original two "conclusions," I think both are true, if we assume all of Hilbert's...
I don't really know how to think about these Smarandache geometries. Jean says that they could be defined on any manifold. It would help me a lot if I could ...
If Smarandache geometries are manifolds, then that helps me, because I can kind of visualize manifolds.<br><br>I really want something to visualize, so if they...
<<I don't really know how to think about these Smarandache geometries.<br> Jean says that they could be defined on any manifold. It would help me a<br>...
<<If Smarandache geometries are manifolds, then that helps me, because I<br> can kind of visualize manifolds.<br><br> I really want something to ...
<I believe that in neutral geometry, given a ray, there is a unique point on<br> the ray at any distance from the endpoint. There is also a ray making ...
First of all, manifolds are the essence of all that is good.<br><br>I think the concept of a manifold started with Riemann. It seems that our minds are ...
<< I'm new too. Because your club is more active than other geometry clubs<br> I enrolled into it.<br><br> Marcelle >><br><br>Merci, Marcelle.<br>I...
Because many messages were dealing with various types of geometries and axioms I thought I need to clarify some definitions.<br><br>DEFINITION 1:<br>Let's have...
<<This makes me think that the axioms for a Smarandache geometry do not<br> require both that lines separate AND that lines intersect just once. This<br>...
<<If Smarandache geometries are manifolds, then that helps me, because I<br> can kind of visualize manifolds.>><br><br>I feel that some of them are...