How can a cylinder be cut and flattened into a rectangle without stretching?

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differential geometry An annular strip (the region between two concentric circles) can be cut and bent into a helical strake that follows approximately the contour of a cylinder. Techniques of differential geometry are employed to find the dimensions of the annular strip that will best match the required curvature of the strake.

In the context of differential geometry, a cylinder can be flattened into a rectangle without stretching because it is a developable surface with a Gaussian curvature of zero.

To achieve this, you must cut the cylinder along one of its vertical straight lines. Because the cylinder's Gaussian curvature is identical to that of a plane (which is also zero), the two surfaces are considered locally isometric. This means the cylinder can be transformed into a flat rectangle without any stretching or distortion of intrinsic distances, as the surface possesses no curvature that would require such deformation to flatten.1