I just want to make sure my understanding is correct. In a "flat" universe, the total density of the universe matches the "critical density". As a result, the universe will expand forever, and never "fall back" into itself. The shape of a flat universe, as the name suggests, is flat like a piece of paper. In a flat universe, the Pythagorean theorem hold true, even when applied to distances of many billions of light years. This is because a flat universe does not curve in any way, except of course for the areas where space-time is curved around massive objects, including black holes. Now for a question: Is it correct to think of the flat universe of a sphere that will never stop expanding? I ask this because, if this is true, then the shape of the universe at any given time would be a sphere, and therefore would in fact be curved. Or should I think of the flat universe as a "cube" that will keep expanding?