# 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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