BRAID ENGINEsubmission case study

01 / 08 · THE QUESTION

How many equal-length connections can a convex polygon hide?

Put n points at the corners of a convex polygon. Join two corners when they are exactly one unit apart. Erdős Problem #96 asks for the largest possible number of joins.

What to take from this step

  1. 1Known constructions make roughly 2n unit-distance pairs.
  2. 2The best published upper bound is about n log₂n.
  3. 3The goal is O(n): at most a fixed constant times n.
PUBLISHED / SOURCE-CHECKEDErdős Problems #96 ↗