Bibliographic Details
| Title: |
The Number of Generalized Balanced Lines. |
| Authors: |
Orden, David1 david.orden@uah.es, Ramos, Pedro1 pedro.ramos@uah.es, Salazar, Gelasio2 gsalazar@dec1.ifisica.uaslp.mx |
| Source: |
Discrete & Computational Geometry. Dec2010, Vol. 44 Issue 4, p805-811. 7p. |
| Subjects: |
Number theory, Line geometry, Mathematical sequences, Set theory, Fixed point theory, Mathematical proofs, Triangles |
| Abstract: |
Let S be a set of r red points and b= r+2 δ blue points in general position in the plane, with δ≥0. A line ℓ determined by them is balanced if in each open half-plane bounded by ℓ the difference between the number of blue points and red points is δ. We show that every set S as above has at least r balanced lines. The proof is a refinement of the ideas and techniques of Pach and Pinchasi (Discrete Comput. Geom. 25:611-628, ), where the result for δ=0 was proven, and introduces a new technique: sliding rotations. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
