jknow: "If you were standing in the sphere and took a photo (using a low distortion lens) what shape would the rectangular frame of the photograph project onto the inside of the sphere? It would look like a rectangle if your eye was in line with the camera sensor, but on the sphere it would be a 3D shape and I'm not smart enough to picture it in my head."
Something like this mirror's shape, except horizontal not vertical:
http://common1.csnimages.com/lf/1/hash/2510/2031295/1/1.jpgThe wider the field of view the more distortion (is it "pincushioning"? I can never remember.... "Pinched").
