Visiting exactly once all the vertices of {0,1,2}^3 with a 13-segment path that avoids self-crossing
In the Euclidean space \(\mathbb{R}^3\), we ask whether one can visit each of the \(27\) vertices of the grid \(G_3:=\{0,1,2\}^3\) exactly once using as few straight-line segments, connected end to end, as possible (an optimal polygonal chain). We give a constructive proof that there exists a \(13\)-segment perfect simple path (i.e., an optimal chain that … Read more