One circle unit that strikes me as strange is the "mils" used for military targeting: there are 6400 mils in a circle. The benefit of this is that 1 meter wide at a distance of 1 kilometer corresponds to 1 mil. So if your tank misses the target by 5 meters and the target is 1 km away, you adjust the angle by 5 mils, nice and easy to compute.

A bit of math shows that this unit is a milliradian (since sin 1/1000 ≈ 1/1000). The strange part is that there should be 6283.18... mils in a circle but that's too inconvenient, so they round it to 6400. In other words, they are using milliradians with the value of 3.2 for π.