“Flat” doesn’t mean “two-dimensional,” it means “not curved.” That is to say, the rules of Euclidean geometry apply to the universe: parallel lines remain parallel forever, the angles of a triangle add up to 180º, you can travel in a straight line forever and not loop back around to where you started, etc. A three dimensional space can be flat or curved in the same way that a two-dimensional surface can be flat or curved: a sheet of paper obeys the aforementioned laws, whereas the surface of a sphere does not. On the curved surface of a sphere, triangles add up to more than 180º, parallel lines eventually intersect, and traveling far enough in a straight line will return you to your starting point. These same principles could apply to a 3D space that’s curved instead of flat.
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