[quote=K-97]
Do you mind explaining Manifolds to me? I remember reading about them at one point (can't remember why?) but I didn't get them 100%.
[/quote]

This is where it gets a little abstract, and I'll admit I'm referencing Wikipedia a bit for guidance on the technical terminology, but essentially a manifold is a space in which every point is like Euclidean space (do you know about Euclidean and non-Euclidean space?). So, essentially, although a manifold as a whole may not exist in Euclidean space, as long as at each point on the object the local area resembles Euclidean space then it's still a manifold.
The best way to describe it is using a sphere, imo - that's how it was explained to me. The surface of a sphere is a 3D non-Euclidean space as a whole, but at each individual point on that surface it looks like a 2D Euclidean space. If you were standing on a sphere (like the Earth), the local area looks like a 2D plane to you, as the curvature is very subtle, and the laws of Euclidean space hold within that local, plane-like area. So, the surface of a sphere is a two-dimensional manifold, because even though the whole thing is non-Euclidean, at each local point it resembles Euclidean space. Note, though, that it only [I]resembles[/I] Euclidean space at each point - the curvature is still there, it's just unnoticeable. A way to understand this is by thinking about map projections of the earth. We can take a small geographic area of the Earth (which will have a subtle curvature and so technically be 3D space) and project it onto a 2D plane - a map. However, the way you transpose it to 2D is dependent on where you are on the curvature - if you then map the same space but standing in a different place, your two maps will differ slightly despite describing the same space, because the 2D projection of the 3D space is merely an approximation and therefore changes defending on your relative perspective.
Of course, all of this gives rise to some pretty cool concepts, and ways to define objects in terms of visualisable space even when those objects exist outside of that. An example is the Klein bottle (yay for wikipedia giving me this example xD), which is actually a 4D object that cannot be implanted in 3D space (though we can [I]represent[/I] it in 3D or even 2D space as a sculpture or drawing), but is actually a 2D-manifold!