Year: 2026
Type: article
Abstract: We present a variation of the broken stick problem in which n stick lengths are sampled uniformly at random. We prove that the probability that no three sticks can form a triangle is the reciprocal of the product of the first n Fibonacci numbers. Extensions to quadrilaterals and general k-gons are also discussed.
Source: The Fibonacci Quarterly
Authors: Aidan Sudbury, Arthur Sun, David Treeby, Edward Wang
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4416920966
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