ive ben wondering about how we seem to think of the shape of the universe if its infinite im really not sure if this is about the possibilities or size or both how ever is its eather one how can any thing infinite have a shape think of a triangle that is infinite it could not be measured and ther for not have a shape if the infinite has to do with possibilites we could never come up with the right one hmm i guess i just dont under stand this hole shape and ifinite thing some one explain please

First of all, please try to organize your thoughts into sentences that are separated by some sort of punctuation.

Now to answer your question, when people talk about the shape of the universe, they are really referring to its

*topology* (sometimes they may be referring to a quantity called its

*metric* but that is not as relevant for what you're getting at).

The topology of the universe can be classified into a few categories. On the highest level, it could be open -- meaning that there exist arbitrarily long straight paths -- or it could be closed, meaning there are all straight-line paths eventually get you back where you started. Ellipsoids and toruses, for example, have closed topologies. The difference between an ellipsoid and a torus is that on a torus there is a closed path (a path that runs into itself eventually) that cannot be shrunk down arbitrarily, whereas on an ellipse, any closed path can be made smaller and smaller as much as you like. (A torus, btw, is basically a donut. It has three kinds of closed paths -- those that go through the hole, those that go around it, and those that avoid it completely. Paths that go through or around the hole obviously cannot be shrunken arbitrarily, but paths that avoid the hole can). This difference between toruses and ellipsoids is called the

*genus* of the surface -- it refers to the number of "handles" that the surface has (e.g. a coffee mug has genus 1, whereas a beach ball has genus 0.)

By contrast, planes, paraboloids, and hyperboloids all have open topologies. If you travel on a straight line on any of these surfaces, you never get back to where you started. Since these surfaces are not closed, it is not meaningful to talk about their genus.

Lastly, there's this notion of a metric -- a special kind of object called a "tensor" that measures the distance between nearby points. Whereas the topology of a surface does not change if you bend the surface without breaking it, once you've specified the metric, no bending is allowed -- the metric truly describes the exact shape (i.e. curvature) of the surface everywhere.

So basically, when people talk about the shape of the universe, they're either talking about its topology or its metric, or both.