2 research outputs found
On diameter bounds for planar integral point sets in semi-general position
A point set in the Euclidean plane is called a planar integral point set
if all the distances between the elements of are integers, and is not
situated on a straight line. A planar integral point set is called to be in
semi-general position, if it does not contain collinear triples. The existing
lower bound for mininum diameter of planar integral point sets is linear. We
prove a new lower bound for mininum diameter of planar integral point sets in
semi-general position that is better than linear
On existence of integral point sets and their diameter bounds
A point set in -dimensional Euclidean space is called an integral
point set if all the distances between the elements of are integers, and
is not situated on an -dimensional hyperplane. We improve the linear
lower bound for diameter of planar integral point sets. This improvement takes
into account some results related to the Point Packing in a Square problem.
Then for arbitrary integers , , we give a
construction of an integral point set of points in -dimensional
Euclidean space, where contains points and such that distance
between and is exactly