A lion and a lion tamer are enclosed within a circular cage. If they move at the same speed but are both restricted by the cage, can the lion catch the lion tamer? (Represent the cage by a circle, and the lion and lion tamer as two point masses within it.)
I am in basic agreement with Daniel. Just to be clear, what he is saying is that the lion, once he reaches the center, is able to always stay between the tamer and the center point, while continuously decreasing the distance between him. Thus, the tamer can never "get past" the lion.
There is one little theoretical detail here. If the lion and the tamer were both dimensionless points, then I believe that the tamer would still be caught by the lion, but it would take an infinite amount of time. Or, to say it differently, if the lion and the tamer were both dimensionless points, then the lion could not catch the tamer. But they are not dimensionless points, and thus it will not take long for part of the tamer to be inside part of the lion.
Raising a small point
