On the number of halving planes
Imre Bárány, Zoltán Füredi, László Lovász · 1989
Let S ⊂ R3 be an n-set in general position. A plane containing three of the points is called a halving plane if it dissects S into two parts of equal cardinality. It is proved that the number of halving planes is at most Ο(n2.998).