15 Dec
2010
15 Dec
'10
8:12 p.m.
Suppose that a closed bounded convex body X in 3-space, with nonempty interior, is such that the area of its orthogonal projection onto any plane is independent of the plane. Does this imply X is a round 3-ball, or are the other examples? What about for higher dimensions? My hunch is that beginning at some dimension, round balls will be the only examples. --Dan Those who sleep faster get more rest.