Published on *Computer Science Department at Princeton University* (http://www.cs.princeton.edu)

In this paper we explore the development of solutions to five key problems in the computational geometry of the plane. The problems we consider were chosen on the basis of their longevity, their significance in computational geometry and the existence of reasonable solutions to each. In each case, the problem

has been actively considered for a decade by both practitioners and theoreticians. The set of problems gives an accurate overview of the problems and methods of computational geometry (in the plane). In most cases, the solutions are practical and we will describe implementation issues. Where appropriate, we discuss extensions to higher dimensions.