The book Proofs without Words is a collection of many short simple proofs, including a construction to trisect a line segment. This short construction naturally leads one to wonder what the shortest construction is (that is, the construction using the least number of circles and lines). We find the shortest trisection of a line segment, then the shortest construction using only circles (Mohr-Mascheroni) and using only lines (Poncelet-Steiner).
This article uses Flash animations to illustrate many of the constructions. You will need a reasonably current version of the Flash Player plug-in installed for your browser in order to view the animations.