Random circles in the d-dimensional unit ball
- 1 June 1989
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 26 (2) , 408-412
- https://doi.org/10.2307/3214047
Abstract
This note gives the solution of the following problem concerning geometric probabilities. What is the probability p(Bd; 2) that the circumference determined by three points P, P1 and P2 chosen independently and uniformly at random in the interior of a d-dimensional unit ball Bd in Euclidean space Ed (d ≧ 2) is entirely contained in Bd? From our result we conclude that p(Bd; 2) →π /(3√3) as d →∞.Keywords
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