You have a box bounded by the planes x=0, x=K, y=0, y=L, z=0, z=M. My intuition is that confining the path to the surface of that box doesn't cost you anything. If that intuition is correct, the answer is sqrt(min((K+L)^2 + M^2, (K+M)^2 + L^2, (L+M)^2 + K^2)). On Mon, Nov 13, 2017 at 7:57 PM, Dan Asimov <dasimov@earthlink.net> wrote:
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
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