Archive for the ‘Geometry’ Category

Cones, Planes, and Automobiles…err…Spheres

Wednesday, May 14th, 2008

Ohh, something new? Well, seeing as I was out of town with essentially nothing to do, I do what I always do: math.

I was looking at an image posted earlier by KC LC with shadows cast by a sphere sitting on a plane. Something stuck out at me which I guess would only stick out if you’ve been staring at conics as long as I have (keep in mind, I’m in aerospace and conics show up big time in orbital mechanics). I noticed that the point of contact between the sphere and plane was pretty damn close to the focus of each of the conic section shadows (I explained the reason for them being conics in a previous comment). While it was easy to demonstrate that the shadows themselves were indeed conics, it’s not nearly as obvious that the point where the sphere touches the plane is a focus of the resulting conic.