# Why is developable surface developable (ie. can be flattened onto a plane without distortion)?

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.

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To learn something about developable surfaces in an historical context you can look at: journals1.scholarsportal.info/details.xqy?uri=/15905896/… –  Joseph Malkevitch Jan 12 '12 at 17:53
@JosephMalkevitch: Uh.. I'm sorry that I cannot get access to that article. –  Roun Jan 13 '12 at 3:43