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?
isometries in 3 dimensions
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isometry
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0Look up [developable surfaces](https://en.wikipedia.org/wiki/Developable_surface). – 2017-01-17
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0"Surface of a square" should be "surface of a cube", don't you think ? – 2017-01-17
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0@JeanMarie: no, square is meant, or any planar rectangle. – 2017-01-17
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0I understand now. Thank you ! – 2017-01-17
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0Another Keyword is "rules surfaces". Among them the one-sheeted hyperboloid and the parabolic hyperboloid. – 2017-01-17