The wonky trammel of Archimedes

This article examines the ellipsograph of Archimedes, also knownas the locus problem of Franciscus van Schooten, and relatedmechanisms. We not only solve the algebraic system explicitly,but we also reverse engineer the problem and find configurationsthat provide a particular solution. Using the modern techniquesof polynomial Gröbner Bases we show this can be used asa traditional compass, as a straight edge (to draw a straightline) and as an ellipsograph to trace ellipses.