How is Gaussian curvature calculated from principal curvatures?

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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 a given point is calculated by taking the product of the two principal curvatures.1

If the principal curvatures are denoted as $κ_{1}$ and $κ_{2}$ , the Gaussian curvature $K$ is defined as:

$K = κ_{1} \times κ_{2}$

These principal curvatures represent the maximum and minimum curvatures of the surface at that point, obtained from sections created by planes containing the surface normal.1