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1.3.2 Global geometry (topology)

In simple words, this is the question which ignores Pythagoras' theorem.

Three different two-dimensional spaces which are all flat spaces, in all of which Pythagoras' theorem is true, are

an infinite flat plane
an infinitely long cylinderThe word cylinder has several meanings. For the geometric object, see Cylinder (geometry . For the engine component, see Cylinder (engine . In firearms the cylinder is the rotating device that contains the firing chambers of a revolver. The phonograph cyl
a 2-torus, i.e. a cylinder with two ends which are defined to be stuck to each other ("identified" with each other)

Each of these is globally very different.

The third is finite in 2-volume, i.e. surface area, but has no edges and Pythagoras' theorem is true everywhere in it.

The Twin paradoxThe Twin paradox is a thought experiment in special relativity. Of two twin brothers one undertakes a long space journey with a very high-speed rocket at almost the speed of light, while the other remains on Earth. When the traveler finally returns to Ear leads to a new paradox in the context of the global shape of space. See the external links for more on this.

1.4 What is the shape of space of our Universe?

We know neither the local nor the global shape of space. We do know that the local shape is approximately flat, just like the Earth is approximately flat. We do not yet know the topology of the universeAccording to the general theory of relativity, spacetime is a pseudo-Riemannian manifold. The term topology of the Universe is generally used to mean the 3- manifold of comoving space, even though strictly speaking, it should probably refer only to the un, and maybe never will.

2 The shape of the whole of space-time

remains to be written

3 External links

Intuition building:

global geometry (topology); requires java (Jeff Weeks' pages)

Texts:

Hints of detections of the shape of the Universe:

Physics

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Topics: Shape Of The Universe Space Geometry Curvature Flat Intuition...

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