Is the Universe Open, Closed, or Flat?

[AntonioLao]

o, true, and that is actually logical.

logical only for Euclidean geometry.

the 5th postulate for Riemannian geometry is that no parallel lines can be constructed.

the 5th postulate for Gaussian geometry is that infinite parallel lines can be constructed.

the latter geometries are properly called non-Euclidean geometries. Einstein's general theory of relativity is based on non-Euclidean geometry due to the nonzero values on either side of the diagonal of the metric tensor indicating positive curvature of spacetime structure.

[Guille]

I sthere any geometry that states that there can be another numnber of paralel lines excluding the other three geometires (zero, one, and infinite)? I mean, with two, three, four....

[AntonioLao]

I sthere any geometry that states that there can be another numnber of paralel lines excluding the other three geometires (zero, one, and infinite)? I mean, with two, three, four....

Starting with n=2, where n is the dimension of the n-dimensional Euclidean space. The number of parallel lines is given by n-1.

1 parallel line for the plane 2D.
2 parallel lines for the cube 3D.
3 parallel lines for the hypercube 4D.
4 parallel lines for the super-hypercube 5D.
5 parallel lines for the super-super-hypercube 6D.

these parallel lines imply orthogonal coordinate axes.

[Guille]

Then, the reiman geometry has infinite dimensions plus one, becuase there are infinite paralel lines?

[AntonioLao]

Then, the reiman geometry has infinite dimensions plus one, becuase there are infinite paralel lines?

You mean Riemann geometry? This is a geometry based on the surface of a sphere where its geodesic lines are great circles. geodesic lines are the shortest and straightest lines for each particular geometry. For the sphere, the geodesics always meet at two points called the poles analogous to the north and south pole of the earth. There are no parallel line on the sphere.

In mathematics, n-dimensional spheres can be defined. Please see the web link for this discussion...

http://mathworld.wolfram.com/Hypersphere.html

[Guille]

The answer is biased by mankind's view of space-time. This view is restricted by the time objects observed, and by a three dimension time object oberver, MAN. The domains in spacetime exhibit behavior in accordance with thier domain properties. This results in an impression of an open unbounded universe, yet the universe is bounded, selfsustaining and quantized.

well, everything will always be biast and from a point of view, but that doesn't mean all are wrong: Especail Relativity. It's the other way round, all are correct, because viewed from here, it is correct to seee spacetime geometric, and gravity as the curve of time, and force as mass times acceleration. And if we were ou of the universe, it would still be a point of view. Even if we were everything: we were god, in every part of the universe and outer space, it would be a point of view, the point of view of someone who sees everything from everywehere everytime at everyplace.

[subversion]

here's a riddle for you
what if the universe was so open that it was closed?

[Guille]

here's a riddle for you
what if the universe was so open that it was closed?

here is my answer..............what if the universe is so open that it is closed, but it becomes so closed that it is opened?

hahaha, good one eee........

[Guille]

o, now I do see the purpose of your antique post.

True, a TOE would have to be a mathematical prove of spacetime from spacetime. But do you think that it owuldn' be geometric viewed from spacetime? do you think gravity eouldn't be the curve of spacetime viewed from space time?

and also, then toe xplain gravity it should be from the point of view of gravity....

and even more, it is reallistically impossiblefor anybody to get completely on another's/thing point of view.

[Unregistered]

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