what does ‘the universe is flat’ mean? How can it be flat when there are stars, planets, galaxies etc. everywhere we look?
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Think of the surface of a sphere, and walking on it. No matter what direction you choose, upon walking far enough you will always return to your starting position, if you continue on in a straight line. This is known as *spherical geometry*, and we say that a surface with this geometry has a *positive* curvature.
There is also *negative* curvature, this is known as *hyperbolic geometry*. It is somewhat harder to explain, but it is often depicted as a sort of ‘saddle-shape’
And finally, there is *zero* curvature, or *euclidean* geometry. Euclidean geometry acts how you’d expect things to act; parallel lines do not diverge (like in hyperbolic geometry) or converge and eventually cross (like in spherical geometry), the interior angles of triangles add up to 180 degrees (which is not so in spherical and hyperbolic geometries), etc.
Now it’s important to distinguish two types of curvature, *local curvature* (which varies place to place) and *global curvature* (which is the same everywhere)
So far as we can tell, our global curvature is zero, or very close to zero.
So the universe ‘being flat’ is not so much a statement about its shape and more a statement of its curvature, or lack thereof
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