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Who first defined curvature using an approximating circle?
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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.
The German mathematician Gottfried Leibniz was the first to define the curvature of a curve at a given point in terms of an approximating circle, which he introduced in 1686.1
Leibniz referred to this circle as the osculating circle—derived from the Latin osculare, meaning "to kiss"—and defined the curvature as the reciprocal of the circle's radius, or . In this framework, a curve that is straighter requires a circle with a larger radius, resulting in a lower curvature value, while a straight line is considered a circle with an infinite radius and zero curvature.1