The premise is basically a 2D plane with a single point, the starting point.
Now a landmark sought by a hiker is a certain distance from that point.
If the hiker can only see 1 mile in any direction, the chance of him finding the landmark by walking straight in a random direction from the starting point seems like it will go down the further away the thing is.
Practically speaking if something is 20 yards from the starting point then any direction I choose to walk I will see it right away. But if something is 20 miles from the starting point then my chance of finding it by walking in a straight line should reduce drastically.
I am imagining a circle that has a radius equal to the distance of the landmark (the center of the circle being the starting point). The further the landmark is, the bigger the circle is, which means if I divide by 360 the 'chunks' will be bigger.
What am I talking about? What's the math for this?
Also, please evaluate my tags, because I am not sure which category this would fall under but I will adjust if you leave a comment (or edit if you have the power).