This post is about trigonometry in the hex-maps used for Traveller subsectors. The summary for those who hate maths is that a jump-4 is actually only 3.46 parsecs if you take the shortest route.
As you can see in the image above is that if you want to go from point X (0503) to point Y (0101) it is a jump-4. The distance is 4 parsecs.
But if you wants to go from point X (0503) to point Z (0103) it is also a jump-4, but the distance is actually shorter since you are zigzagging when you are counting the hexes following the dotted orange line.
How much shorter is it? If we use Pythagoras, then:
a2 + b2 = c2
b2 = c2 – a2
b2 = 16 – 4 = 12
b = 3.46
If we use trigonometry, b = 4 * cos(30) = 3.46.
In the Adventures of the Starship Notorious the crew meets a very talented jump-drive scientist that helps the crew improve and calibrate their J-3 drive so that it can do 3.46. This will only work if the ship is unloaded and if a special jump-program is run.