Median Area for Broken Sticks

Steven R. Finch

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arXiv · 1804.09602

Median Area for Broken Sticks

Steven R. Finch

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Abstract

Breaking a line segment L in two places at random, the three pieces can be configured as a triangle T with probability 1/4. We determine both the PDF and CDF for area(T) in terms of elliptic integrals. In particular, if L has length 1, then the median area 0.031458... can be calculated to arbitrary precision. We also mention the analog involving cyclic quadrilaterals -- with corresponding probability 1/2 -- and ask some unanswered questions.

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Steven R. Finch. 2018-04-25. Median Area for Broken Sticks. https://arxiv.org/abs/1804.09602

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