Some Dual Problems of Geometric Probability in the Plane

A definition is adopted for convexity of a set of directed lines in the plane. Following this, the duals of a number of standard problems of geometric probability are formulated. Problems considered in detail are the duals of Sylvester's problem, chord length distributions and Ambartzumian's combinatorial geometry. The paper suggests some questions for further work.

A simulation study of Sylvester's problem in three dimensions

This note gives estimates of solutions to the Sylvester problem in three dimensions. These results suggest that the solutions in four and higher dimensions are very close to the solution for the n -dimensional sphere which is known.

A simulation study of Sylvester's problem in three dimensions

This note gives estimates of solutions to the Sylvester problem in three dimensions. These results suggest that the solutions in four and higher dimensions are very close to the solution for the n -dimensional sphere which is known.