Hi,
This topic is simple. What sort of place is Equestria in a geometric sense? By this I mean to ask if Equestria lies on a plane, or a sphere, or whatever, as the show leaves it rather unclear and has at times hinted in more than one direction. I would like to discuss evidence and arguments that might help solve this question, and also to promote my own view that Equestria must lie on a flat plane. Thus, I feel that we may as well jump right in. First I'll give reasons to think that Equestria is flat, and then some counter-evidence that rebuts my claim.
For a flat Equestria:
Celestia and Luna are said to "raise the sun" and "raise the moon" respectively, and we have even seen Celestia do so in the show on one occasion. Furthermore, we also witnessed the sun and moon rapidly moving across the sky when Discord was playing around with everything.
Think about what that would mean for a spherical Equestria. The first implication is that by "raising the sun" over one part of the globe, you'd be lowering it for the opposite side, which while possible, runs contrary to the idea of truly "raising the sun". Furthermore, by raising the sun on a spherical Equestria, that implies that (if heliocentric) the sun is actually rotating about the sphere (and Celestia controls the motion of a massive body at will), or (if geocentric) that Celestia is controlling the rotation of the planet itself, which is a no less improbable proposition.
As a final point, we should note that the sun/moon move rapidly when being raised, and even more rapidly when they were under the influence of Discord. As I said before, on a spherical Equestria view, this involves the rapid movement of some really big objects, which seems improbable for a single pony (even an alicorn) to accomplish.
For a spherical Equestria:
We once saw a model globe in an episode.
There is reference to the cardinal directions in the show, which makes a lot more sense with a geocentric sphere model.
There we are. Now assuming that this thread is in the right place, and that some of you have thoughts on this issue... Discuss!