The number of generalized balanced lines

• David Orden ^[1] ; Pedro Ramos ^[1] ; Gelasio Salazar ^[2]
  1. [1] Universidad de Alcalá

     Universidad de Alcalá

     Alcalá de Henares, España

     
  2. [2] Universidad Autónoma de San Luis Potosí

     Universidad Autónoma de San Luis Potosí

     México

     
• Localización: XIII Encuentros de Geometría Computacional: Zaragoza, del 29 de junio al 1 de julio de 2009 / coord. por Alfredo García Olaverri, Javier Tejel Altarriba, 2009, ISBN 978-84-92774-11-1, págs. 229-233
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.