A curved surface in a two-dimensional world can appear strange, as every observer is confined to those two dimensions only.
However, consider the surface of a globe. It's a curved surface, easily perceivable in our three-dimensional space but experienced differently in only two dimensions.
The curvature of a surface forms depending on how it bends in space.
- A positively curved surface (like a sphere) bends away from the plane, causing geometric rules, like those for angles in a triangle, to change.
- A negatively curved surface (like a saddle) instead bends towards the plane differently, also altering geometric principles.
In these different curved surfaces, triangles will not have the typical 180-degree angle sum, providing a clear way to identify the type of world one inhabits.