Why?
The length of the chain is pi.
The dog can move both ways around the lighthouse.
When he gets halfway he still has pi/2 length to move, and can continue his sweep. Back to the beginning.
Moving the other way, the same happens, and he has some overlapping areas.
I think the diagrams shown are not that accurate, in that they only show what happens with a pi/2 leash.
And, I've been wrong before.
Arf