This Demonstration illustrates the four-point problem of J. J. Sylvester (1814–1897). He presented the problem in the April 1864 issue of Educational Times;
see , [2, pp. 15–21]. The problem was as follows: if we pick four points at random inside some given convex region, what is the probability that the four points are the vertices of a concave quadrilateral? Wilhelm Blaschke (1885–1962) showed that the probability is at least
and at most
, depending on the form of the convex region. W. S. B. Woolhouse (1809–1893) showed that the lower bound is achieved if the convex region is a circle; for a square, the probability is
and for a regular hexagon,
. The Demonstration is based on , where a method is presented to generate random points in a circle.
 P. J. Nahin, Digital Dice: Computational Solutions to Practical Probability Problems
, Princeton, NJ: Princeton University Press, 2008.