Treasure Hunt

[VictorB212]

Problem: There is a point in a sphere with radius 90k-110k. You have a ship with a radar of radius 47k. What is the best search pattern to fly in order to find the point with the least flying?

I've been thinking about this and have come up with a few ideas. The roughest is of course to fly a cube pattern and totally brute force it. Refining that a little, we fly the "latitudes," trying to find the point. However, I just came up with the idea that if one were to fly each edge of an icosahedron with diameter ~ 180k, then things might be more efficient.

First, I would like feedback on the search mechanism. Second of all, does anyone know how to calculate side length and anle measurement when given a certain diameter (vertex to opposite vertex) of an icosahedron?

[kedaman]

If you want to optimize the course of covering the whole volume at shortest path, most of the course would be traversing the inner side of the sphere in a spiral motion, without leaving any spot, so the intersection area of the radar and the sphere inner side(and thus the distance to the side) would play a crusial role in how many revolutions would be needed to cover the Peripheral volume, but also the radius of the path (which would be increasing towards the equator).

If theres any point in finding the spot earlier with a higher probability but having a longer course to cover the whole volume then you could try the same strategy but with leaving part of the sides, especially at the endpoints of the course