Can You Really Derive Conic Formulae from a Cone?

Editor's Note: This article was originally published in the inaugural edition of Convergence in April of 2004. We are pleased to "reprint" it in June of 2015 with 17 interactive GeoGebra applets that take advantage of GeoGebra's new 3D capability, hosted by GeoGebraTube.

In this article we will see how ancient Greek geometers discovered and constructed conic sections. The modern equations of the conic sections are derived from Greek sources using only high school mathematics, mostly the theory of similar triangles. We also make use of GeoGebra to better illustrate the relationships involved in the derivations.