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Why does a straight line have zero 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 curvature of a curve is defined as the reciprocal of the radius of its osculating circle—the circle that most closely approximates the curve at a given point.12
As a curve becomes straighter, the radius of this approximating circle must increase. In the limit, a straight line is mathematically treated as a circle with an infinite radius. Because the curvature is defined as , as the radius approaches infinity, the curvature approaches zero. Consequently, a straight line is defined as having zero curvature everywhere.12