Imagine you are on an (in)finite 2d-plane (and confined to walk on it). There's a straight line somewhere on the plane, but you don't know where it is and neither can you find it by looking from afar. You have to cross it! What's the best walking strategy to find the line in the least time possible?
Edited: As of @Brandon_J and @Adam answers which close the question for the infinite plane, please consider answering the best strategy for the finite plane case. (If it is not a good policy to edit the scope of the question this way, please edit it back.)
- Choose a random direction and walk for a distance of $r$
- Walk now along the circle of radius $r$
- If after the full circle you haven't met the line, increase the distance from the starting point by another amount of $r$
- Walk along the circle of radius $2r$
- Repeat the procedure until you cross the line