Walking in circles

We show that for every x1, . . . , xn, y1, . . . , yn ∈ S1 there exists i ∈ {1, . . . , n} such that n k=1 d(xi, xk) ≤ n k=1 d(xi, yk), where S1 is the unit circle and d is the distance on S1 . We also discuss a game theoretic interpretation of this result.

• Type: Journal
• Year: 2010
• Where: DM
• Authors: Noga Alon, Michal Feldman, Ariel D. Procaccia, Moshe Tennenholtz
• Keywords: DM 2008, DM 2010, Game, Theoretic, Unit Circle