A digestion of unit distance constructions

🫧 Open on Bubbles Suppose that one has a set of points in the plane, which we will think of as the complex plane . Let denote the number of unit distances determined by these points, i.e., pairs of points whose displacement obeys the equation (For this discussion it will not be important whether we count the pair separately from .) The Erdös unit distance problem asks, for a given large number , what is the largest possible value of amongst all sets of cardinality