I may have derived this from the travellermap API document or come up with it myself, I don't remember now, but it works.

I have a mathematica method toMap[] which will take a vector of the x and y hex number and return a map-space value: 

toMap[vec_] := Module[{ix, iy, x, y},
   ix = vec[[1]] - 0.5;
   iy = If[ EvenQ[ vec[[1]] ], vec[[2]] - 0.5, vec[[2]] ];
   x = ix Cos[\[Pi] 6^-1];
   y = -iy;
   {x, y}
   ];

then just take the regular euclidean distance between them, e.g.,

In[972]:= EuclideanDistance[ toMap[{01,01}], toMap[{08,10}] ]
Out[972]= 10.4403

Asking mathematica for a general solution gives:

In[973]:= EuclideanDistance[ toMap[{ax,ay}], toMap[{bx,by}] ]
Out[973]= Sqrt[Abs[1/2 Sqrt[3] (-0.5+ax)-1/2 Sqrt[3] (-0.5+bx)]^2+Abs[-ay+by]^2]

where ax, ay are the hex coordinates of the first hex and bx, by are the coordinates of the second 

On Fri, Mar 27, 2020 at 3:33 PM Jeff Zeitlin <xxxxxx@freelancetraveller.com> wrote:

Given a standard Traveller subsector, with coordinates 0101 to 0810,
alternate columns staggered, what's the formula/algorithm to calculate the
jump distance between two hexes?

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