A New Engineering for the Perfect Compass and Its Use in Mathematics Education

In this paper we deal with a geometric machine that has gone somewhat unnoticed in mathematics education: the Perfect Compass. It allows conics to be drawn using a special two aperture compass, based on Apollonius' conic sections. Proposed in the 10th century, it seems that it was never built in medieval times--at least no archaeological remains from the medieval period have been found--and later constructions have operational limitations. This machine has been reengineered by us to make it fully functional and thus become a suitable instrument for education. We have built it using Digital Manufacturing technology, such as 3D printing and laser cutting, so that it can be widely available in the service of mathematics education. We also show how its operation results in a machine where its manipulation allows direct knowledge of the method and concepts used.