Acute triangles in the n-ball
- 1 September 1982
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 19 (03) , 712-715
- https://doi.org/10.1017/s0021900200037244
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 ℝ n , 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.Keywords
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