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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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  • $\begingroup$ Look up developable surfaces. $\endgroup$ – Ivan Neretin Jan 17 '17 at 8:22
  • $\begingroup$ "Surface of a square" should be "surface of a cube", don't you think ? $\endgroup$ – Jean Marie Jan 17 '17 at 9:24
  • $\begingroup$ @JeanMarie: no, square is meant, or any planar rectangle. $\endgroup$ – exp8j Jan 17 '17 at 12:00
  • $\begingroup$ I understand now. Thank you ! $\endgroup$ – Jean Marie Jan 17 '17 at 16:29
  • $\begingroup$ Another Keyword is "rules surfaces". Among them the one-sheeted hyperboloid and the parabolic hyperboloid. $\endgroup$ – Jean Marie Jan 17 '17 at 16:32

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