A classic! I’m working on the Culture novels now, which have their own variant (“orbitals”), minus the shadow squares or central star. Can’t recommend them enough, so far.
Orbitals, while enormous (greater surface area than earth), are much smaller. The Culture novels do have Ringworld-sized rings as well, though. E.g. from Consider Phlebas, flying under the orbital Vavatch: "It was like flying upside-down over a planet made of metal; and of all the sights the galaxy held which were the result of conscious effort, it was one bested for what the Culture would call gawp value only by a big Ring, or a Sphere."