Quite simply, I'm wondering what would be the best projection to use for a map of a Ring World. Distortion would be nonexistent as far as I can tell, and it would only need the left and right edges to match. The map would span 12,742 km from north to south and 940,000,000 km from east to west (approximately). Given the large scales couldn't I use a flat projection for any resonably sized area?

On a side note, does anyone know of an easy way to wrap a fractal terrain around a ring instead of a sphere?