In this paper, we construct a single hyperbola G that, along with a straight edge and compass, allow for the trisection of any angle. Descartes constructed a parabola with this property in his original treatment of analytic geometry. Unlike Descartes's proof, the proof that all angles can be trisected with the hyperbola G is a geometric rather than an algebraic argument.
Prof. Lawrence Smolinsky, Department of Mathematics, Louisiana State University
Fink, Julie and Molbert, Nicholas
"Sectioning Angles Using Hyperbolic Curves,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 14
, Article 13.
Available at: http://scholar.rose-hulman.edu/rhumj/vol14/iss1/13