You are at the edge of an enormous circular arena. A hungry lion is eying you from the centre of this area. You are both capable of running at the same maximum speed, but constraint within the arena. The lion has worked out a strategy of always running at maximum speed in an outward direction such that he stays positioned on the line thru you and the center of the arena.
The starting signal sounds and the lion starts moving. You can't outrun the lion. How do you ensure you stay out of the lion's claws?
- the arena is truly gigantic, and you can think of you and the lion as point objects constrained within a circle of unit radius
- there is no latency in the lion's reactions to your movements: at any moment in time you, the lion, and the center of the arena remain co-linear
- the lion catches you if, and only if, his position coincides with yours
Running at maximum speed along any circular path centered on the center of the arena is not going to help you. Starting from the center, the lion will run at the same speed along a circular path of half the radius and catch you as soon as you have completed a quarter of a circle. (It is easy to check that these paths keep you, the lion and the center co-linear.)