[math-fun] Distance across integer coordinate planes

13 Nov 2017

      Let W denote the union of all coordinate planes given by

  x  =  K

or

  y  =  K

or

  z  =  K

for K an integer.  I.e.,

   W  =  Z x R x R  u  R x Z x R  u  R x R x Z

with Z = integers, R = reals.

Question:
---------

   Let P, Q belong to Z^3.  

   What is the length of the shortest path connecting P to Q that lies entirely in W ???

           *                    *                    *

WLOG assume P = (K,L,M) and Q = (0,0,0).  The answer is a function of form f(K,L,M).

What is f(K,L,M) ???

I'm not sure if this is easy or hard.

—Dan

Dan Asimov