The Bottom of the Universe isn’t Euclidean.
In the words of the great dragon Maliutka Malkh, recorded in Kohg vs. World, “Slodoop is the bottom of the universe, the place planets go when they die.” In that tale we also discover that, in Slodoop, a perfectly straight line may intersect itself. These observations deserve more explanation.
The universe has a bottom. That bottom extends infinitely outward and has an infinite sky above it, with an infinite number of stars and galaxies. The bottom is remarkably terrestrial, with gravity, mountains, lakes, forests, and sunshine, each of which deserves additional discussion.
The gravity at the bottom of the universe is in the neighborhood of 10 meters per second per second and points down, implying there is slightly more mass below the bottom of the universe (i.e., in the ground) than there is above it (i.e., in the stars). Efforts to determine what is under ground have so far failed, nor has the question of the amount of star gravity the ground needs to counter been adequately answered.
Gravity is constant. It does not vary with location or altitude, as parallel waves do not dissipate. Every single star and planet in the universe is accelerating toward Slodoop at approximately 10 m/s2. However, there is no consequent blue shift as would be predicted by Einstein’s theory of relativity, nor do stars visibly move in the sky within a single human’s lifespan.
Slodoop has earth-like terrain, for the most part, with mountain ranges, jungles, forests, deserts, rivers, lakes, and ponds. It doesn’t have any real seas; there are lakes a few hundred miles across and a few hundred feet deep; there are even a few salt lakes in deserts, but there are no oceans. Almost all lakes have outlets into further rivers, though some have only inlets and maintain their level through evaporation.
Slodoop’s climate changes smoothly over the thousand mile scale, ranging from arctic to tropical temperatures though most are in the temperate to sub-tropical range. Seasons also cycle smoothly, though not at the same rate everywhere; years of three to four hundred days are common.
Slodoop doesn’t have any sun, moon, ring, or satellites of any kind. There aren’t any planets or comets in the sky, and stars don’t move season to season or hour to hour.
However, Slodoop does have sunlight, strong parallel rays of light that illuminate the entire bottom of the universe at once. The slope of this light move from horizontal to near-azimuth and down to the horizon again every day, with lingering atmospheric after-glow for hour-long twilights, but there isn’t a strong sense of east or west. At any given point, the sun will rise and set in consistent directions, but what those directions are varies widely over just a few miles.
There is no general way to navigate by the sky. Just as the east and west wander about freely as you travel, so to do the locations of the stars. Those familiar with an area can use those star patterns to tell location as well as direction, but those skills do not extend to unfamiliar locations.
Slodoop does not have a flat geometry. Some areas are larger than their circumference would suggest, while others are smaller. These irregularities can change, though usually they do so over the course of centuries, not years. Topologists have not been able to determine any consistent higher-dimensional embedding for the areas they have measured.
That said, if you were dropped in Slodoop you wouldn’t even notice things weren’t flat. Out to several hundred yards the curvature is close to constant, providing a stable-looking view even under generous motion. It’s only when you try to make a map or take a shortcut that the curvature of Slodoop’s geometry can mess you up.
A simple rule of thumb is that all paths will curve toward “large” spaces and away from “small” spaces.
There are exceptions to the not-visibly-curved rule. Magic can coax space to warp in particular ways, so there really are houses that are larger on the inside, and still will be even if the house itself is removed.