It started with a Dyson Shell/Sphere. There were precursors to the idea but in 1959 Freeman Dyson published a paper in which he claimed that a sufficiently advanced society would eventually need the total energy output of their star and would envelop it with energy collector satellites. The idea was that any light from that star would be altered to reflect the building materials OR that we'd be getting radiation from the civilization and the star, but no light. The point of this thought experiment was to indicate what we should be looking for in our search for planets with life.
Others took this Dyson Sphere, connected the satellites, and made it solid enough for people to live on the inside of the shell. This is the commonly known model. If you put too much thought into it you'll start to see issues with this idea. Such as the fact that only the equator would be habitable since you'd need to spin the sphere to provide gravity. The further you go from the equator the more this simulated gravity would pull to the side and the thinner the air would get.
Larry Niven advanced the idea with the creation of a Niven Ring or Ringworld. Imagine a hula hoop big enough for the Sun. Make it big enough to fill Earth's orbit. After all, if we're going to live on it it has to be not too near (too hot) and not too far (too cold). It needs to be in what some call the Goldilocks Zone.
In the book "Ringworld" Larry Niven explores a ringworld built by a now missing alien species. He covers the weather pattern differences in a non-spherical world, the defense systems, and even what happens if society collapses and doesn't have anything to mine since the world is manufactured.
It's one of the great sci-fi books. Most sci-fi readers would put it in their 10 ten favorite books. It's a world unlike any you've heard of. As you continue to explore it inspires the reader to continually slap their head with all the problems and advantages that would come from such a world. Some issues remain and engineering students made sure that Niven heard about it. The second book remedy's these problems. I wouldn't recommend going beyond book two.
The Dyson Sphere appeared in an episode of Star Trek: The Next Generation when they found Scotty's shuttle craft crashed on the outer surface.
The Niven Ring is the basis for the video game "Halo".
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