Sylvester's Four-Point Problem

Pick random points from a region, then find the convex hull. What are the odds that all the generating points are on the boundary of the hull? In 1865, Sylvester stated, "This problem does not admit of a determinate solution." Actually, the answer depends on the region. Four points from a triangular region have odds of of making a quadrilateral. Four points from a rectangular region have odds of of making a quadrilateral.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.