Abstract
Using Baddeley's [1] extension of Crofton's differential equation we derive an elementary integral formula for the probability that three randomly chosen points in the unit n-ball in ℝn, with respect to Lebesgue measure, form an acute triangle. When the dimension is 2 this probability is 4/π2 − 1/8, while when the dimension is 3 it is 33/70.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
25 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Visibility phenomena in hypercubes;Chaos, Solitons & Fractals;2023-10
2. How Likely is a Random Triangle Acute?;Resonance;2023-08-16
3. Taming Spatial Complexity;Spatial Complexity;2020
4. Hall’s Conjecture on Extremal Sets for Random Triangles;The Journal of Geometric Analysis;2019-05-10
5. Random triangles in planar regions;Rendiconti del Circolo Matematico di Palermo Series 2;2018-07-17