Inspired by a childrens game.
Two points $p_1$ and $p_2$ are hidden at two random locations with real coordinates $(x,y)$ in a coordinate system. A point-like representation of you is placed at the origin. The objective is to find the coordinates of the two points.
$D$ = (the distance between you and $p_1$)$+$(the distance between you and $p_2$).
You are allowed to move in the plane in any direction any length of distance.
The only sources of information is your position on the plane and wether $D$ is increasing, decreasing, or staying the same. This information is recieved continiously.
Is there a method to always find the coordinates of $p_1$ and $p_2$?
What is the least number of times needed to change direction in order to guarrantee that the coordinates are found?
For only one point, the least number of times needed to change direction is 3. For motivaton, see comments.
Similar to in the one-point case, the origin can in the two-point case be thought of as a point on a tilted ellipse with foci $p_1$ and $p_2$.
For the same sort of problem in one dimension on the number line: The cases with 1 and 2 points are trivial, but for 3+ points, it is impossible to find a general method.
For the same sort of problem in three dimensional space: The case with 1 point can be solved in a manner similar to the the case with 1 point in two dimensions by finding two cicles on the surface of a sphere centered at $p$. Will elaborate.