The Number of Generalized Balanced Lines

Let S be a set of r red points and b = r +2 blue points in general position in the plane. A line determined by them is said to be balanced if in each open half-plane bounded by the difference between the number of red points and blue points is . We show that every set S as above has at least r balanced lines. The main techniques in the proof are rotations and a generalization, sliding rotations, introduced here.

• Type: Journal
• Year: 2010
• Where: DCG
• Authors: David Orden, Pedro Ramos, Gelasio Salazar
• Keywords: Blue Points, DCG 2010, General Position, Red Points