The course Differential Geometry told me that developable surfaces, of which the Gaussian curvature is $0$, can be flattened onto a plane without distortion.
Some says this is because a developable surface can have the same metric as a plane. But I still think metric here is a little abstract, since I can't figure out the connection between metric and the physical nature or the structure of a paper.
I cannot connect well between the physical phenomenon of paper folding and its mathematical description of Gaussian curvature or metric.
Is there a good physical explanation of this? Thanks.