Please Prove This Beautiful Result

The expected projected area of a convex set S in 3-dimensional space is 1/4 of the surface area of S.

Special case is S is a ball. surface area is 4*pi*R*R.

It's OK not being able to prove it, but we have to say it's very beautiful.

所有跟帖： 

• 什么分布呀 -康MM- ♀ (0 bytes) () 06/13/2007 postreply 14:55:01

• Must be uniform distribution -Commentate- ♂ (0 bytes) () 06/13/2007 postreply 19:51:15

• 可能就是用那个球来证明吧。 很希望看到精确证明 -乱弹- ♂ (0 bytes) () 06/13/2007 postreply 16:22:24

• Hint 1 -Commentate- ♂ (73 bytes) () 06/14/2007 postreply 06:52:13

• Hint 2 -Commentate- ♂ (159 bytes) () 06/14/2007 postreply 06:53:00

• I thought a small area dS would be considered..... -乱弹- ♂ (0 bytes) () 06/14/2007 postreply 09:22:39

• I start to doubt this result. -Commentate- ♂ (0 bytes) () 06/14/2007 postreply 14:10:35