Concerning an interesting shadow and conic sections?

Question

Recently, i was in the Albany capitol building on the million dollar staircase, and i looked on the cieling. There was a parabolic arch with the vertex a bit below the cieilng, and beyond that a cieling formed a kind of dome. The interesting thing about this was that the light, which was situated right in front of the arch, created a shadow on the dome behind it that, instead of creating a parabolic shadow, created quite the opposite, two shadowy curves going opposite directions, so that they came together at a cusp, and not a curve. How could this happen?

Answer 1

Some really pretty patterns can occurs with the smoothness of curves and shadows. Conic sections are the intersection of a plane with a cone. Imagine the intersection of light, which is planar at our distance from the sun, with a more complicated shape. That's what you were observing.