  Real quadric curves are often referred to as "conic sections," implying that
they can be realized as plane sections of circular cones. However, it seems
that the details of this equivalence have been partially forgotten by the
mathematical community. The definitive analytic treatment was given by Otto
Staude in the 1880s and a non-technical description was given in the first
chapter of Hilbert and Cohn-Vossen's "Geometry and the Imagination" (1932). The
main theorem is elegant and easy to state but is surprisingly difficult to find
in the literature. A synthetic version appears in The Universe of Conics (2016)
but we still have not found a full analytic treatment written down. The goal of
this note is to fill a surprising gap in the literature by advertising this
beautiful theorem, and to provide the slickest possible analytic proof by using
standard linear algebra that was not standard in 1932.
