Evading Equilateral Triangles without a Map
Braxton Carrigan · 2010
Consider an arrangement of equilateral non-overlapping translated triangles in the plane and two points S and T so that the segment ST is parallel to a side of each of the triangles. Assume one needs to navigate from point S to point T by evading the triangular obstacles without any previous knowledge of the location of the obstacles. The navigator becomes aware of a triangle once it is contacted along the path. The given algorithm enables the navigator to reach the target point T by a path with length less than √ 3d(1 + 2 d2), where d is the length of ST. 1