High Quality Content by WIKIPEDIA articles! In mathematics, the Crofton formula, named after Morgan Crofton (1826–1915), is a classic result of integral geometry relating the length of a curve to the expected number of times a "random" line intersects it.Suppose ? is a rectifiable plane curve. Given an oriented line l, let n?(l) be the number of points at which ? and l intersect. We can parametrize the general line l by the direction ? in which it points and its signed distance p from the origin. Both sides of the Crofton formula are additive over concatenation of curves, so it suffices to prove the formula for a single line segment. Since the right-hand side does not depend on the positioning of the line segment,

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