Advertisement

Combinatorica

, Volume 16, Issue 4, pp 567–573 | Cite as

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

  • Pavel Valtr
Article

Abstract

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

Mathematics Subject Classification (1991)

Primary: 60 D 05 Secondary: 52 A 22 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    I. Bárány: The limit shape of convex lattice polygons,Discrete and Computational Geometry 13 (1995), 279–295.Google Scholar
  2. [2]
    M. G. Kendal, andP. A. P. Moran:Geometrical probability, Griffin, London, 1963.Google Scholar
  3. [3]
    L. Lovász:Combinatorial problems and exercises, Akadémiai Kiadó, Budapest, 1979.Google Scholar
  4. [4]
    G. Rote: The limit shape of random convex sets, draft.Google Scholar
  5. [5]
    L. A. Santaló:Integral Geometry and Geometric Probability, Addison-Wesley, Reading, Massachusetts, 1976.Google Scholar
  6. [6]
    P. Valtr: Probability thatn random points are in convex position,Discrete and Computational Geometry,13 (1995), 637–643.Google Scholar
  7. [7]
    W. Weil, andJ. A. Wieacker: Stochastic geometry, Chapter 5.2 in: P.M. Gruber and J.M. Wills (eds.),Handbook of Convex Geometry, II, North-Holland (1993), 1393–1438.Google Scholar

Copyright information

© Akadémiai Kiadó 1996

Authors and Affiliations

  • Pavel Valtr
    • 1
  1. 1.Department of Applied MathematicsCharles UniversityPraha 1Czech Republic

Personalised recommendations