Starship in half-space
Source: Moscow mathematic olympiad 2022, P11.4
September 29, 2022
geometry
Problem Statement
The starship is in a half-space at a distance from its boundary. The crew knows about it, but has no idea in which direction to move in order to reach the boundary plane. The starship can fly in space along any trajectory, measuring the length of the path traveled, and has a sensor that sends a signal when
the border has been reached. Can a starship be guaranteed to reach the border with a path no longer than ?