The 2-dimensional surface of a square can be isometrically transformed into a 3-dimensional cylinder or a cone. In what other shapes can it be isometrically transformed? More generally, what is the underlying theory concerning isometric transformations of surfaces in 3 dimensions?
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Look up developable surfaces. – Ivan Neretin Jan 17 '17 at 08:22
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"Surface of a square" should be "surface of a cube", don't you think ? – Jean Marie Jan 17 '17 at 09:24
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@JeanMarie: no, square is meant, or any planar rectangle. – exp8j Jan 17 '17 at 12:00
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I understand now. Thank you ! – Jean Marie Jan 17 '17 at 16:29
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Another Keyword is "rules surfaces". Among them the one-sheeted hyperboloid and the parabolic hyperboloid. – Jean Marie Jan 17 '17 at 16:32