I remember this as a classic problem, but all Google results are video-game-related, so I guess I should ask it here:
An adventurer got lost in the desert, but he knew that there was a highway exactly 10 miles from him. What path should he follow in order to find the highway as fast as possible (on average)?
Assumptions: (1) The adventurer would find the highway when his path intersects with it. (2) The speed of the adventurer is constant.
And what about the high-dimensional case, where the adventurer is lost in a n-dimensional space trying to find a (n-1)-dimensional superplane?
My guess for the 2D case is an Archimedean spiral but I can't prove it. For higher dimensional cases it seems really hard and I've no idea.
Thanks!