I have recently started learning the differential geometry of curves and surfaces.
I am not sure what intrinsic/extrinsic means.
My current understanding is this: an intrinsic quantity on a curve is one that is determined by its shape, so does not change with rotation and translation.
Based on this understanding, the curvature at a point is an intrinsic quantity and the x-coordinate of that point is an extrinsic quantity.
On the other hand, a friend of mine says that curvature is an extrinsic quantity because curves are isometric to straight lines.
What is the standard definition of intrinsic/extrinsic?