Repeated angles in three and four dimensions

Abstract

Abstract. We show that the maximum number of occurrences of a given angle in a set of n points in � 3 is O(n 7/3), and that a right angle can actually occur Ω(n 7/3) times. We then show that the maximum number of occurrences of any angle different from π/2 in a set of n points in � 4 is O(n 5/2 β(n)), where β(n) = 2 O(α(n)2) and α(n) is the inverse Ackermann function