TY - JOUR

T1 - Repeated angles in three and four dimensions

AU - Apfelbaum, Roel

AU - Sharir, Micha

PY - 2005

Y1 - 2005

N2 - We show that the maximum number of occurrences of a given angle in a set of n points in ℝ 3 is O(n 7/3) and that a right angle can actually occur n(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 ℝ 4 is O(n 5/2β(n)), where β(n) = 2 O(α(n) 2) and α(n) is the inverse Ackermann function.

AB - We show that the maximum number of occurrences of a given angle in a set of n points in ℝ 3 is O(n 7/3) and that a right angle can actually occur n(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 ℝ 4 is O(n 5/2β(n)), where β(n) = 2 O(α(n) 2) and α(n) is the inverse Ackermann function.

KW - Combinatorial geometry

KW - Geometric incidences

KW - Repeated angles

UR - http://www.scopus.com/inward/record.url?scp=33646829444&partnerID=8YFLogxK

U2 - 10.1137/S0895480104443941

DO - 10.1137/S0895480104443941

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AN - SCOPUS:33646829444

SN - 0895-4801

VL - 19

SP - 294

EP - 300

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 2

ER -