what is the shape of space?

WHAT IS THE SHAPE OF SPACE?We are used to thinking of space as the emptiness in which things happen, like an empty warehouseready to be filled, or a theater stage on which the events of the Universe play out.
But General Relativity predicts that space is not just emptiness, it is a physical,dynamic thing, and that prediction has been borne out by many, many experiments.Space can bend because of matter and energy, curving the paths of objects that move insideof it.
It can ripple with gravitational waves And it can expand, creating more and more spacebetween two objects.All of these phenomena can be described by one idea: curvature of space (or spacetime).In flat regions of spacetime (like, if there as no energy or matter nearby), objects travelingalong parallel paths stay along parallel paths.
In positively curved regions of spacetime (like near planets or black holes), parallelpaths converge, and in negatively curved regions of spacetime parallel paths (or even pathspointed at each other!) diverge.But what about space as a whole ?
If space is positively curved everywhere, then there only one shape space can be: a giant hyper-potato.If you went in one direction for long enough, eventually you end up in the same placeyou started.If space is flat everywhere, its shape could be simple: just extend out straight to infinity.Or it could loop around in a periodic way, like in some video games:And if space is negatively curved everywhere, sports would be impossibleSo which is it?There are basically two ways to measure the large-scale curvature of the Universe.

One is to measure the angles inside of triangles.If the space is flat, then the angles will add up to 180 degrees.But if the space is curved, those angles will add up to more or less than 180 degrees dependingon the type of curvature.Cosmologists have done the equivalent of measuring our Universes triangles by looking at apicture of the early Universe, and studying the spatial relationship between differentpoints on that picture.The second way to measure curvature is to measure the thing that causes space to curvein the first place: the density of energy and matter throughout the Universe.Which cosmologists have also measured.

It turns out that in both cases, measurements show the Universe to be pretty much flat(within 0.4% margin of error).But before you get disappointed that we don't live in a cool cosmic hyper-potato, let metell you one big problemThe fact that we live in a flat Universe appears to be a GIGANTIC, COSMIC-LEVEL COINCIDENCE.If the Universe had just a little bit more mass and energy, space would have curved oneway.And if it had just a little bit less mass and energy, space would have curved the otherway.But we seem to have just the right amount to make space perfectly flat as far as wecan tell.

This perfect amount is the equivalent of five hydrogen atoms per cubic meter of space, onaverage.
If instead there were six hydrogen atoms per cubic meter of space on average, or four,the entire Universe would have been a lot more curved or a lot less .
And we so far have no idea why our universe has the density that it does.When it comes to the curvature of the universe, our knowledge falls flat.