Danzer set

Unsolved problem in mathematics:
Does a Danzer set with bounded density or bounded separation exist?
Construction of a two-dimensional Danzer set with growth rate from overlaid rectangular grids of aspect ratio 1:1, 1:9, 1:81, etc.

In geometry, a Danzer set is a set of points that touches every convex body of unit volume. Ludwig Danzer asked whether it is possible for such a set to have bounded density.[1][2] Several variations of this problem remain unsolved.[3]

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