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The probability thatn random points in a triangle are in convex position

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Abstract

We show thatn random points chosen independently and uniformly from a triangle are in convex position with probability

$$\frac{{2^n (3n - 3)!}}{{((n - 1)!)^3 (2n)!}}$$

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Authors and Affiliations

  1. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    Pavel Valtr

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  1. Pavel Valtr
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Additional information

This research was supported by the Czech Republic Grant GAČR 201/94/2167 and by the Charles University grants Nos. 351 and 361.

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Valtr, P. The probability thatn random points in a triangle are in convex position. Combinatorica 16, 567–573 (1996). https://doi.org/10.1007/BF01271274

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  • DOI: https://doi.org/10.1007/BF01271274

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