In 1596, Johannes Kepler proposed a model of the solar system built around the idea of the platonic solids. The theory had to be abandoned for several reasons, but from his research, he discovered that the orbits of our planets were ellipses rather than circles. In his mind, this was an “ugly” theorem, but there is in fact a beautiful mathematical formalism for ellipses — as two-dimensional slices of a cone, or “conic sections”. In this demonstration, you can move a two-dimensional plane in 3D space, intersecting it in various ways with two cones. The intersecting region(s) are outlined, allowing you to see the many kinds of conic sections possible.