Ringworld
A ribbon of extremely strong material surrounding a G-type star (Sunlike) at a distance of approximately 153 million kilometers, or a little over 1 AU, making a radius of 961 million kilometers. It is approximately 1.6 million kilometers across, making for a total inner surface area of 1.538*10^15 square kilometers.
This arrangement provides a surface area millions of times that of Earth, all with incoming solar radiation equivalent to an Earthlike planet. A ring of large sunshades called shadow squares closer to the star than the Ringworld gives a day-night cycle. In order to live on such a structure, however, the builders must provide several other important elements.
Gravity for the inhabitants is created by spinning the ringworld in uniform circular motion, the acceleration due to the change in the direction of velocity can be abstracted as a single centrifugal "force" in the moving object's rest frame, equal to mv^2/r. The rest frame of the ringworld already includes two forces. One is the gravitational attraction of the star, the other is the centrifugal force of a naturally orbiting body. They exactly cancel each other out, so further calculations will come from this as a rest frame.
In order to provide Earthlike gravity on the inner surface, the Ringworld needs to be spinning at roughly 1249 kilometers a second linear velocity at the edge. Needless to say, this is extremely fast.
Walls at the rims 1600 kilometers high are sufficient to hold an atmosphere in, and a habitable environment is now available.
There are a few technical difficulties with this structure:
The stresses such an artifact would undergo are so strong that the tensile strength of its construction material (called Scrith by Niven) approaches that of the strong nuclear force.
After construction, the Ringworld must be spun up to the correct speed. The total kinetic energy in the Ringworld is 1.6*10^39 joules. This is equal to the entire energy output of a Sunlike star for 130,000 YEARS. Clearly, spinning the Ringworld is a major undertaking.
Inside the ring, the gravitational forces from the mass of all parts of the ring will exactly cancel itself out. Therefore, gravity will not keep the Ringworld centered around the star, and some sort of attitude jets will be needed.
While in most situations the centrifugal force simulates planetary gravity nearly exactly, there are a few extra factors to consider. Fast-moving objects heading with or away from the spin will actually increase or decrease in apparent weight. Since this change is proportional to the ratio between the object speed and the Ringworld's speed, this change will be slight for most operations, but, like the Coriolis forces on Earth, it can build up over thousands of kilometers and create massive "eye storms," like horizontal hurricanes.
See also Dyson Sphere.
