Random circles in the d-dimensional unit ball

Random circles in the d-dimensional unit ball

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Article ID: iaor1990667
Country: Israel
Volume: 26
Issue: 2
Start Page Number: 1
End Page Number: 7
Publication Date: Jun 1989
Journal: Journal of Applied Probability
Authors:
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 results we conclude that p(Bd;2)⇒;/(3√″3â) ad d⇒•.

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