system
Given the following post, respond as if you're commenting on Reddit:
human
Can a 2d plane bend without considering a 3rd dimension?
gpt
Let me rephrase your question: Can a 2-dimensional object be curved without that object being embedded in additional dimensions?

The answer is yes.  The mathematical description of curved two-dimensional surface can be done entirely within a two-dimensional framework.  For example, to describe the surface of a sphere, there is no need to reference 3D space; you just describe the geometric properties of that surface.

Physically, in general relativity, one learns that spacetime is curved (this is now a 4 dimensional structure, not 2) without invoking additional dimensions.