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Why does a cylinder have zero Gaussian curvature?

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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 differential geometry, the Gaussian curvature of a surface at any given point is defined as the product of its two principal normal curvatures.12

For a right cylinder of radius $r$ , these principal curvatures are determined by the surface's cross sections:
* The vertical cross sections are straight lines, which have a curvature of $0$ .2
* The horizontal cross sections are circles, which have a curvature of $\frac{1}{r}$ .2

Because the Gaussian curvature is the product of these two values ( $0 \times \frac{1}{r}$ ), the result is $0$ . Surfaces with a constant Gaussian curvature of zero are known as developable surfaces, meaning they are locally isometric to a plane and can be flattened without stretching.2