I’m asking you WHY ARE YOU THINKING THIS!!!!! I guess your just really smart like that. And like death rays. ]]>

-PF

]]>The unbounded conics could never practically cast a fully circular shadow; at least not as far as I can imagine. At the very least the cast shadow will be a portion of a circle. What might be slightly more interesting is placing a pinhole camera at the vertex of the cone, pointed along the cone’s axis. In this case, a parabola would form a complete circle (well, with the exception of a single point). Hyperbolas still wouldn’t form complete circles.

]]>What about the reverse problem? I’ve read before that all conics can cast a circular shadow. Easy to see this for an ellipse. What about the others?

]]>The type of conic section depends on the source’s position with respect to a plane tangent to the top of the sphere (or, in general, tangent to the sphere and opposite from and parallel to the shadow receiving plane). If the light source is on the far side of this plane from the shadow receiver, you get an ellipse. If it’s on the plane, you get a parabola. If it’s below the plane (but not below the sphere), you get a hyperbola.

]]>Here’s something sort of related… to conic sections anyway: shadows from a sphere. Place a sphere on a plane, then place lights in various locations to cast shadows. Depending on the light locations, the shadow will be a circle, ellipse, parabola, or one branch of a hyperbola:

http://www.flyingbanjo.com/temp/conic_shadows.png

I left out the circle (too obvious). The light location to get an elliptical shadow is pretty obvious too. But less obvious with the parabola and hyperbola. I know the positions needed for them, but I haven’t tried to prove it.

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