Sets of points with the property that no two elements of the set are one unit distance apart are called unit-distance avoiding sets. If a point is in the unit-distance avoiding set, then the unit circle drawn around it does not intersect the set, but there is no restriction regarding the interior and the exterior of this circle. When searching for unit-distance avoiding sets with high densities, the following construction naturally comes to mind: an open disc with a unit diameter is unit-distance avoiding, as all distances between its two points are less than 1.