In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, the Hanan grid H(S) of a finite set S of points in the plane is obtained by constructing vertical and horizontal lines through each point in S.

The main motivation for studying the Hanan grid stems from the fact that it is known to contain a rectilinear Steiner tree

Rectilinear Steiner tree

The rectilinear Steiner tree problem, minimum rectilinear Steiner tree problem , or rectilinear Steiner minimum tree problem is a variant of the geometric Steiner tree problem in the plane, in which the Euclidean distance is replaced with the rectilinear distance...

for S. It is named after M. Hanan, who was first to investigate the rectilinear Steiner minimum tree and introduced this graph.