, Volume 16, Issue 4, pp 567-573

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

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

We show thatn random points chosen independently and uniformly from a triangle are in convex position with probability $$\frac{{2^n (3n - 3)!}}{{((n - 1)!)^3 (2n)!}}$$ .

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