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 -