Unwrapping Curves from Cylinders and Cones

@article{Apostol2007UnwrappingCF,
  title={Unwrapping Curves from Cylinders and Cones},
  author={T. Apostol and M. Mnatsakanian},
  journal={The American Mathematical Monthly},
  year={2007},
  volume={114},
  pages={388 - 416}
}
Now imagine the elliptical cross section replaced by any curve lying on the surface of a right circular cylinder. What happens to this curve when the cylinder is unwrapped? Consider also the inverse problem, which you can experiment with by yourself: Start with a plane curve (line, circle, parabola, sine curve, etc.) drawn with a felt pen on a rectangular sheet of transparent plastic, and roll the sheet into cylinders of different radii. What shapes does the curve take on these cylinders? How… Expand
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