what does it mean when people say the universe is flat?
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Look at a piece of paper compared to a globe. The paper is flat, the globe is curved. While not exactly intuitive or easy to comprehend, there is an equivlance to this in 3D (whereas the paper and glove are 2D).
To tell the difference, we can use triangles. Triangles in flat space have angles that sum 180 whereas in curved space they can sum to different amounts (e.g. a triangle on a globe can have sums greater than 180).
By calculating the positions to and between distant celestial objects we can form triangles and measure their angles. Within a high degree of accuracy, these measurements imply we live in a flat, 3D universe.
Flat in this case doesn’t mean literally 2 dimensional like a piece of paper. What we mean by flat here is not curved. In other words, the universe obeys Euclidean geometry. This is the geometry we’re all most familiar with in our daily lives, i.e., parallel lines never meet and the sum of angles in a triangle is always 180 degrees.
Something that’s not flat is curved. Think of the surface of a sphere. On the surface of a sphere, parallel lines will always meet and the sum of angles in a triangle is not 180 degrees. In this analogy, the surface of a sphere is a 2D representation of what curved 3D space would be like.
Our measurements point to our universe being flat or extremely close to flat.
Just means there’s people who think the Universe is not spherical. But there’s no way to know that it is or isn’t right now.
A simplification of the other comments:
If you held a laser perfectly parallel to the ground, and there were no trees or mountains or buildings in the way, that laser beam would eventually go off into space, right? Because the Earth is round but the laser beam is perfectly straight, so the beam would keep going rather than follow the curve of the Earth.
As far as we can tell, there’s no such “curve” to the universe as a whole. If our laser beam kept going through space, it wouldn’t eventually go off into… outside-the-universe.
Gravity is curvature in space-time, so when physicists talk about the “shape” of the universe, they’re talking about how much gravity there is.
In a “closed”/”elliptic” universe, there’s enough gravity that all the matter and energy will eventually end up in the same place: the universe that began with a Big Bang will end in a Big Crunch. In terms of curvature, what this means is that if you shine two locally-parallel laser beams out into space, their paths will get gradually closer together and eventually cross (like two locally-parallel lines on the surface of a sphere).
In an “open”/”hyperbolic” universe, there’s so little gravity that the universe will expand faster and faster over time: the universe that began with a Big Bang will end in a Big Rip. In terms of curvature, what this means is that if you shine two locally-parallel laser beams out into space, their paths will get gradually further and further apart from one another (like two locally-parallel lines on the surface of a saddle).
A flat/”Euclidian” universe is one perfectly balanced between these two possibilities: there’s enough gravity to eventually bring the expansion of the universe arbitrarily close to a stop, but not enough to actually reverse that expansion. In terms of curvature, what this means is that if you shine two locally-parallel laser beams out into space, they will remain at a constant distance from one another indefinitely (like two parallel lines on a flat sheet of paper).
Here’s a Wikipedia picture that might help: [link](https://upload.wikimedia.org/wikipedia/commons/4/44/Comparison_of_geometries.svg) .
You can imagine a 2D space being flat (like a piece of paper, the top of a table, or anything people usually call flat) or curved, like the surface of a curved object (a sphere for example). One way to check if it’s flat, is that the angles of a triangle must add to 180° and the circumference of a circle must be 2πr. If it’s curved, it’s not the case.
In the same way, a 3D space can be flat or curved around a 4th inaccessible dimension. The way to check if it’s curved is to check the angles of a triangle, the ratio between the circumference of a circle and its radius, or some other things.
The 3D space is approximately flat around low gravity objects, and curved around high gravity objects like black holes.
The observable universe (if you check as far as you can from Earth in all directions) is perfectly flat at the precision we can observe it. So if we check a circle or triangle on the CMB (lights coming from the farthest we can see, which is also the earliest we can see) it is flat.
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