Solution to the Dead Fly Problem

Key Points

• To prove that in any set of points intersecting a convex region of area 1, pairs must exist at arbitrarily small distances.
• Used a packing argument to analyze spatial arrangements of points.
• Applied interval analysis to assess distances between points.
• Employed scaling techniques to derive contradictions regarding minimum distances.
• Demonstrated that arbitrary point sets interacting with convex regions require close distances.
• Proved that the minimum distance between some pairs of points must be zero.