Ok, I thought about this and discussed it with a friend.
I think that from the point I am viewing myself in the mirror, suppose I am looking myself in the eye, the rest of my head would be proportional to the actual size of my head, and be flared along the side of the sphere.
Suppose I stood with my arms and legs extended outward, my fingertips would be reflected like a normal mirror and from there my arm would be flared and warped with the rest of the mirror, like my head. This would continue along the mirror until the reflection of my back and eventually my legs.
The mirrors on my right side would reflect my head like it did the front. Suppose my ear and the farthest point from the center of the sphere form a straight line, the very center of my ear (or the endpoint of this line) would be undistorted, and the rest of the right side of my head would flare throughout the mirror, proportionately.
Now this leads to my ultimate question: how many of me would there be? My first thought was there would be 360 of me, one for each degree. Also there may be 8 or 16 of me, or maybe 32, one for each general direction from which my body can be viewed.
I'll have to ask my chemistry teacher this one. Man this is gonna keep me up tonight...
I think that from the point I am viewing myself in the mirror, suppose I am looking myself in the eye, the rest of my head would be proportional to the actual size of my head, and be flared along the side of the sphere.
Suppose I stood with my arms and legs extended outward, my fingertips would be reflected like a normal mirror and from there my arm would be flared and warped with the rest of the mirror, like my head. This would continue along the mirror until the reflection of my back and eventually my legs.
The mirrors on my right side would reflect my head like it did the front. Suppose my ear and the farthest point from the center of the sphere form a straight line, the very center of my ear (or the endpoint of this line) would be undistorted, and the rest of the right side of my head would flare throughout the mirror, proportionately.
Now this leads to my ultimate question: how many of me would there be? My first thought was there would be 360 of me, one for each degree. Also there may be 8 or 16 of me, or maybe 32, one for each general direction from which my body can be viewed.
I'll have to ask my chemistry teacher this one. Man this is gonna keep me up tonight...