Summary: Walking in Circles
Noga Alon
Michal Feldman
Ariel D. Procaccia
Moshe Tennenholtz §
Abstract
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.
1 Introduction
Let x1, . . . , xn, y1, . . . , yn R, and denote N = {1, . . . , n}. We claim that there exists i N such
that
kN
|xi - xk|

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

Collections: Mathematics