Re: "Real" ringworlds
OK, so apparently a Niven-esque ringworld is technically impossible since the materials required cannot physically exist.
How about an Orbital from the Culture novels? They look like ringworlds, except that they don't encircle the star, they just orbit it in the same way a planet does. They are much smaller (only a few hundred thousand or million miles across, if memory serves, although that still offers many multiples Earth's surface area) and because the star isn't at the centre of the ring, all the night/day problems are avoided straight off.
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