Can search area for a set of 3 known co-ords be calculated?
Yes, but is this really a signal triangulation? I am not into the game archaeology stuff yet so I have not enough background information to make an estimated method of approach.
If you only got 3 positions without any source signal, you can only guess what the "rule" for finding a fourth position may be. Unless some clue was given somewhere. The more data, the more accurate the method of approach will be.
Maybe we should use our ears in space, listen for the signal, if there is any.
We could guess that the perfect plane build from the 3 positions "is" the search area ( including the points and the borders ). Or, we can assume that the perpendicular "prism" constructed as a triangular cylinder in both directions is the search area.
Without a fourth position, there is just too many solutions. But we could start the search on and near the three positions, for any clues on how to progress further.
If we do have a signal, we can calculate the angular plane and therefore a more precise direction of the "prism"/triangular cylinder search area. If we know the speed and behavior of that type of signal we can also calculate distance to the source, which gives only two solutions, one on each side of the search plane. That is enough to actually find it, by just sending scout parties to both locations.
But the optimal situation is to find 'a' fourth position (as in 3 and 1 more ).
For realism, we actually need to do this in 4-space. Where we also take time into consideration. Stellar formations move around, swirls and does not keep their stellar patterns over thousands of years as many believe. Its more like a fluid motion ever changing. Therefore it is nearly impossible to actually do any "ancient triangulation", unless we know all the relative variables. We can come close, as we project and calculate the movement of our own planets in the Sol system, but it only takes one single stray big object from outer space, anywhere in time, to disrupt the predicted outcome. And we know space do provide those stray objects over time. See the signal as a beam of "light", it is afflicted by gravitational lensing, diffraction, refraction etc etc. Over time, a clear laser-signal would look more like background noise than any clear signal, also extremely weak and diluted by every other signal from the same direction over time.
For the purpose of the difficulty set by FD, I assume it is a plain linear logic in 3-space only. But maybe a simple linear time factor somewhere for increased difficulty, just not too difficult.
but I do wonder what made Jaques' massive jump stop there though - he was aiming for the other side of the galaxy after all. Clearly there is some kind of anomaly around Colonia to pull him out of his jump maybe the other end of whatever we have here at this end.
