I kid,
But as others have stated, the ring is an entity of its own and will adjust to fit the person who currently has it. The ring was also created by Sauron, so as he wears it he has more control over it than others would which leads me to believe that he (Sauron) can choose whether to be invisible or not.
I am guessing on this last part as I read the books so long ago I don't remember if it gives an explanation on that aspect.
Yes, I love LOTR, and yes I am a nerd.