geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

, the Hanan grid of a

finite set In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example, :\ is a finite set with five elements. T ...

of points in the plane is obtained by constructing vertical and horizontal lines through each point in . The main motivation for studying the Hanan grid stems from the fact that it is known to contain a minimum length

rectilinear Steiner tree The rectilinear Steiner tree problem, minimum rectilinear Steiner tree problem (MRST), or rectilinear Steiner minimum tree problem (RSMT) is a variant of the geometric Steiner tree problem in the plane, in which the Euclidean distance is replaced w ...

for . It is named after Maurice Hanan, who was first to investigate the rectilinear Steiner minimum tree and introduced this graph.M. Hanan
On Steiner's problem with rectilinear distance
J. SIAM Appl. Math. 14 (1966), 255 - 265.

References

{{reflist Graph families Geometric graphs